First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization

Abstract We use asymptotic analysis to describe in a more systematic way the behavior at the infinity of functions in the convex and quasiconvex case. Starting from the formulae for the first- and second-order asymptotic function in the convex case, we introduce similar notions suitable for dealing...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Flores-Bazán, F. [verfasserIn] Hadjisavvas, N. [verfasserIn] Lara, F. [verfasserIn] Montenegro, I. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2016

Schlagwörter:	Quasiconvexity Asymptotic functions Second-order asymptotic functions and cones Optimality conditions Nonconvex optimization

Übergeordnetes Werk:	Enthalten in: Journal of optimization theory and applications - Dordrecht [u.a.] : Springer Science + Business Media, 1967, 170(2016), 2 vom: 27. Apr., Seite 372-393
Übergeordnetes Werk:	volume:170 ; year:2016 ; number:2 ; day:27 ; month:04 ; pages:372-393

Links:	Volltext

DOI / URN:	10.1007/s10957-016-0938-6

Katalog-ID:	SPR015011550

Internformat


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520			\|a Abstract We use asymptotic analysis to describe in a more systematic way the behavior at the infinity of functions in the convex and quasiconvex case. Starting from the formulae for the first- and second-order asymptotic function in the convex case, we introduce similar notions suitable for dealing with quasiconvex functions. Afterward, by using such notions, a class of quasiconvex vector mappings under which the image of a closed convex set is closed, is introduced; we characterize the nonemptiness and boundedness of the set of minimizers of any lsc quasiconvex function; finally, we also characterize boundedness from below, along lines, of any proper and lsc function.
650		4	\|a Quasiconvexity \|7 (dpeaa)DE-He213
650		4	\|a Asymptotic functions \|7 (dpeaa)DE-He213
650		4	\|a Second-order asymptotic functions and cones \|7 (dpeaa)DE-He213
650		4	\|a Optimality conditions \|7 (dpeaa)DE-He213
650		4	\|a Nonconvex optimization \|7 (dpeaa)DE-He213
700	1		\|a Hadjisavvas, N. \|e verfasserin \|4 aut
700	1		\|a Lara, F. \|e verfasserin \|4 aut
700	1		\|a Montenegro, I. \|e verfasserin \|4 aut
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912			\|a GBV_ILN_26
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4328
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
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matchkey_str	article:15732878:2016----::isadeodreaypoiaayiwtapiainiq
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bklnumber	31.80
publishDate	2016
allfields	10.1007/s10957-016-0938-6 doi (DE-627)SPR015011550 (SPR)s10957-016-0938-6-e DE-627 ger DE-627 rakwb eng 330 510 000 ASE 31.80 bkl Flores-Bazán, F. verfasserin aut First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We use asymptotic analysis to describe in a more systematic way the behavior at the infinity of functions in the convex and quasiconvex case. Starting from the formulae for the first- and second-order asymptotic function in the convex case, we introduce similar notions suitable for dealing with quasiconvex functions. Afterward, by using such notions, a class of quasiconvex vector mappings under which the image of a closed convex set is closed, is introduced; we characterize the nonemptiness and boundedness of the set of minimizers of any lsc quasiconvex function; finally, we also characterize boundedness from below, along lines, of any proper and lsc function. Quasiconvexity (dpeaa)DE-He213 Asymptotic functions (dpeaa)DE-He213 Second-order asymptotic functions and cones (dpeaa)DE-He213 Optimality conditions (dpeaa)DE-He213 Nonconvex optimization (dpeaa)DE-He213 Hadjisavvas, N. verfasserin aut Lara, F. verfasserin aut Montenegro, I. verfasserin aut Enthalten in Journal of optimization theory and applications Dordrecht [u.a.] : Springer Science + Business Media, 1967 170(2016), 2 vom: 27. Apr., Seite 372-393 (DE-627)266883923 (DE-600)1468244-8 1573-2878 nnns volume:170 year:2016 number:2 day:27 month:04 pages:372-393 https://dx.doi.org/10.1007/s10957-016-0938-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 170 2016 2 27 04 372-393
spelling	10.1007/s10957-016-0938-6 doi (DE-627)SPR015011550 (SPR)s10957-016-0938-6-e DE-627 ger DE-627 rakwb eng 330 510 000 ASE 31.80 bkl Flores-Bazán, F. verfasserin aut First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We use asymptotic analysis to describe in a more systematic way the behavior at the infinity of functions in the convex and quasiconvex case. Starting from the formulae for the first- and second-order asymptotic function in the convex case, we introduce similar notions suitable for dealing with quasiconvex functions. Afterward, by using such notions, a class of quasiconvex vector mappings under which the image of a closed convex set is closed, is introduced; we characterize the nonemptiness and boundedness of the set of minimizers of any lsc quasiconvex function; finally, we also characterize boundedness from below, along lines, of any proper and lsc function. Quasiconvexity (dpeaa)DE-He213 Asymptotic functions (dpeaa)DE-He213 Second-order asymptotic functions and cones (dpeaa)DE-He213 Optimality conditions (dpeaa)DE-He213 Nonconvex optimization (dpeaa)DE-He213 Hadjisavvas, N. verfasserin aut Lara, F. verfasserin aut Montenegro, I. verfasserin aut Enthalten in Journal of optimization theory and applications Dordrecht [u.a.] : Springer Science + Business Media, 1967 170(2016), 2 vom: 27. Apr., Seite 372-393 (DE-627)266883923 (DE-600)1468244-8 1573-2878 nnns volume:170 year:2016 number:2 day:27 month:04 pages:372-393 https://dx.doi.org/10.1007/s10957-016-0938-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 170 2016 2 27 04 372-393
allfields_unstemmed	10.1007/s10957-016-0938-6 doi (DE-627)SPR015011550 (SPR)s10957-016-0938-6-e DE-627 ger DE-627 rakwb eng 330 510 000 ASE 31.80 bkl Flores-Bazán, F. verfasserin aut First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We use asymptotic analysis to describe in a more systematic way the behavior at the infinity of functions in the convex and quasiconvex case. Starting from the formulae for the first- and second-order asymptotic function in the convex case, we introduce similar notions suitable for dealing with quasiconvex functions. Afterward, by using such notions, a class of quasiconvex vector mappings under which the image of a closed convex set is closed, is introduced; we characterize the nonemptiness and boundedness of the set of minimizers of any lsc quasiconvex function; finally, we also characterize boundedness from below, along lines, of any proper and lsc function. Quasiconvexity (dpeaa)DE-He213 Asymptotic functions (dpeaa)DE-He213 Second-order asymptotic functions and cones (dpeaa)DE-He213 Optimality conditions (dpeaa)DE-He213 Nonconvex optimization (dpeaa)DE-He213 Hadjisavvas, N. verfasserin aut Lara, F. verfasserin aut Montenegro, I. verfasserin aut Enthalten in Journal of optimization theory and applications Dordrecht [u.a.] : Springer Science + Business Media, 1967 170(2016), 2 vom: 27. Apr., Seite 372-393 (DE-627)266883923 (DE-600)1468244-8 1573-2878 nnns volume:170 year:2016 number:2 day:27 month:04 pages:372-393 https://dx.doi.org/10.1007/s10957-016-0938-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 170 2016 2 27 04 372-393
allfieldsGer	10.1007/s10957-016-0938-6 doi (DE-627)SPR015011550 (SPR)s10957-016-0938-6-e DE-627 ger DE-627 rakwb eng 330 510 000 ASE 31.80 bkl Flores-Bazán, F. verfasserin aut First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We use asymptotic analysis to describe in a more systematic way the behavior at the infinity of functions in the convex and quasiconvex case. Starting from the formulae for the first- and second-order asymptotic function in the convex case, we introduce similar notions suitable for dealing with quasiconvex functions. Afterward, by using such notions, a class of quasiconvex vector mappings under which the image of a closed convex set is closed, is introduced; we characterize the nonemptiness and boundedness of the set of minimizers of any lsc quasiconvex function; finally, we also characterize boundedness from below, along lines, of any proper and lsc function. Quasiconvexity (dpeaa)DE-He213 Asymptotic functions (dpeaa)DE-He213 Second-order asymptotic functions and cones (dpeaa)DE-He213 Optimality conditions (dpeaa)DE-He213 Nonconvex optimization (dpeaa)DE-He213 Hadjisavvas, N. verfasserin aut Lara, F. verfasserin aut Montenegro, I. verfasserin aut Enthalten in Journal of optimization theory and applications Dordrecht [u.a.] : Springer Science + Business Media, 1967 170(2016), 2 vom: 27. Apr., Seite 372-393 (DE-627)266883923 (DE-600)1468244-8 1573-2878 nnns volume:170 year:2016 number:2 day:27 month:04 pages:372-393 https://dx.doi.org/10.1007/s10957-016-0938-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 170 2016 2 27 04 372-393
allfieldsSound	10.1007/s10957-016-0938-6 doi (DE-627)SPR015011550 (SPR)s10957-016-0938-6-e DE-627 ger DE-627 rakwb eng 330 510 000 ASE 31.80 bkl Flores-Bazán, F. verfasserin aut First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We use asymptotic analysis to describe in a more systematic way the behavior at the infinity of functions in the convex and quasiconvex case. Starting from the formulae for the first- and second-order asymptotic function in the convex case, we introduce similar notions suitable for dealing with quasiconvex functions. Afterward, by using such notions, a class of quasiconvex vector mappings under which the image of a closed convex set is closed, is introduced; we characterize the nonemptiness and boundedness of the set of minimizers of any lsc quasiconvex function; finally, we also characterize boundedness from below, along lines, of any proper and lsc function. Quasiconvexity (dpeaa)DE-He213 Asymptotic functions (dpeaa)DE-He213 Second-order asymptotic functions and cones (dpeaa)DE-He213 Optimality conditions (dpeaa)DE-He213 Nonconvex optimization (dpeaa)DE-He213 Hadjisavvas, N. verfasserin aut Lara, F. verfasserin aut Montenegro, I. verfasserin aut Enthalten in Journal of optimization theory and applications Dordrecht [u.a.] : Springer Science + Business Media, 1967 170(2016), 2 vom: 27. Apr., Seite 372-393 (DE-627)266883923 (DE-600)1468244-8 1573-2878 nnns volume:170 year:2016 number:2 day:27 month:04 pages:372-393 https://dx.doi.org/10.1007/s10957-016-0938-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 170 2016 2 27 04 372-393
language	English
source	Enthalten in Journal of optimization theory and applications 170(2016), 2 vom: 27. Apr., Seite 372-393 volume:170 year:2016 number:2 day:27 month:04 pages:372-393
sourceStr	Enthalten in Journal of optimization theory and applications 170(2016), 2 vom: 27. Apr., Seite 372-393 volume:170 year:2016 number:2 day:27 month:04 pages:372-393
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Quasiconvexity Asymptotic functions Second-order asymptotic functions and cones Optimality conditions Nonconvex optimization
dewey-raw	330
isfreeaccess_bool	false
container_title	Journal of optimization theory and applications
authorswithroles_txt_mv	Flores-Bazán, F. @@aut@@ Hadjisavvas, N. @@aut@@ Lara, F. @@aut@@ Montenegro, I. @@aut@@
publishDateDaySort_date	2016-04-27T00:00:00Z
hierarchy_top_id	266883923
dewey-sort	3330
id	SPR015011550
language_de	englisch
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author	Flores-Bazán, F.
spellingShingle	Flores-Bazán, F. ddc 330 bkl 31.80 misc Quasiconvexity misc Asymptotic functions misc Second-order asymptotic functions and cones misc Optimality conditions misc Nonconvex optimization First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization
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topic_title	330 510 000 ASE 31.80 bkl First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization Quasiconvexity (dpeaa)DE-He213 Asymptotic functions (dpeaa)DE-He213 Second-order asymptotic functions and cones (dpeaa)DE-He213 Optimality conditions (dpeaa)DE-He213 Nonconvex optimization (dpeaa)DE-He213
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title	First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization
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title_full	First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization
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title_sort	first- and second-order asymptotic analysis with applications in quasiconvex optimization
title_auth	First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization
abstract	Abstract We use asymptotic analysis to describe in a more systematic way the behavior at the infinity of functions in the convex and quasiconvex case. Starting from the formulae for the first- and second-order asymptotic function in the convex case, we introduce similar notions suitable for dealing with quasiconvex functions. Afterward, by using such notions, a class of quasiconvex vector mappings under which the image of a closed convex set is closed, is introduced; we characterize the nonemptiness and boundedness of the set of minimizers of any lsc quasiconvex function; finally, we also characterize boundedness from below, along lines, of any proper and lsc function.
abstractGer	Abstract We use asymptotic analysis to describe in a more systematic way the behavior at the infinity of functions in the convex and quasiconvex case. Starting from the formulae for the first- and second-order asymptotic function in the convex case, we introduce similar notions suitable for dealing with quasiconvex functions. Afterward, by using such notions, a class of quasiconvex vector mappings under which the image of a closed convex set is closed, is introduced; we characterize the nonemptiness and boundedness of the set of minimizers of any lsc quasiconvex function; finally, we also characterize boundedness from below, along lines, of any proper and lsc function.
abstract_unstemmed	Abstract We use asymptotic analysis to describe in a more systematic way the behavior at the infinity of functions in the convex and quasiconvex case. Starting from the formulae for the first- and second-order asymptotic function in the convex case, we introduce similar notions suitable for dealing with quasiconvex functions. Afterward, by using such notions, a class of quasiconvex vector mappings under which the image of a closed convex set is closed, is introduced; we characterize the nonemptiness and boundedness of the set of minimizers of any lsc quasiconvex function; finally, we also characterize boundedness from below, along lines, of any proper and lsc function.
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title_short	First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization
url	https://dx.doi.org/10.1007/s10957-016-0938-6
remote_bool	true
author2	Hadjisavvas, N. Lara, F. Montenegro, I.
author2Str	Hadjisavvas, N. Lara, F. Montenegro, I.
ppnlink	266883923
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doi_str	10.1007/s10957-016-0938-6
up_date	2024-07-03T13:23:16.272Z
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First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization

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