Theorems of the Alternative for Systems of Convex Inequalities

被引：10

作者：

Arutyunov, Aram V. ^{[1
]}

Zhukovskiy, Sergey E. ^{[1
]}

Marinkovic, Boban ^{[2
]}

机构：

[1] RUDN Univ, 6 Miklukho Maklaya St, Moscow 117198, Russia

[2] Univ Belgrade, Fac Technol & Met, Dept Math Sci, Belgrade, Serbia

来源：

SET-VALUED AND VARIATIONAL ANALYSIS | 2019年 / 27卷 / 01期

关键词：

Theorem of the alternative; Solvability conditions; Systems of convex inequalities; OPTIMALITY CONDITIONS;

D O I：

10.1007/s11228-017-0406-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Systems of convex inequalities in function spaces are considered. Solvability conditions are obtained in the form of a theorem of the alternative. We revisit some results from the literature where such theorems are incorrect. We present counterexamples concerning these results and by introducing some regularity conditions we obtain new theorems which are dedicated to solvability of systems of convex inequalities.

引用

页码：51 / 70

页数：20

共 24 条

[1]

Alekseev VM., 1987, OPTIMAL CONTROL, DOI 10.1007/978-1-4615-7551-1

[2]

[Anonymous], 2011, Introduction to the theory of multivalued maps and differential inclusions

[3]

[Anonymous], 1977, OPTIMAL CONTROL MATH

[4]

[Anonymous], 2011, MATH EC FINANCE

[5]

Arutyunov A.V., 2000, Optimality condition: abnormal and degenerate problems

[6]

Aubin J.P., 1990, Set-Valued Analysis, DOI 10.1007/978-0-8176-4848-0

[7] Nonsmooth continuous-time optimization problems: Necessary conditions [J].

Brandao, AJV ;

Rojas-Medar, MA ;

Silva, GN .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2001, 41 (12) :1477-1486

[8]

Clarke FH., 1983, OPTIMIZATION NONSMOO

[9] Continuous-time optimization problems involving invex functions [J].

de Oliveira, V. A. ;

Rojas-Medar, M. A. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 327 (02) :1320-1334

[10] Continuous-time multiobjective optimization problems via invexity [J].

De Oliveira, Valeriano A. ;

Rojas-Medar, Marko A. .

ABSTRACT AND APPLIED ANALYSIS, 2007,

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