On Nonsmooth Semi-Infinite Minimax Programming Problem with (Φ, ρ)-Invexity

被引：0

作者：

Liu, X. L. ^{[1
]}

Lai, G. M. ^{[2
]}

Xu, C. Q. ^{[3
]}

Yuan, D. H. ^{[1
]}

机构：

[1] Hanshan Normal Univ, Dept Math, Chaozhou 521041, Guangdong, Peoples R China

[2] Hanshan Normal Univ, Dept Comp Sci, Chaozhou 521041, Guangdong, Peoples R China

[3] Beijing Univ Civil Engn & Architecture, Coll Sci, Beijing 102616, Peoples R China

来源：

ABSTRACT AND APPLIED ANALYSIS | 2014年

关键词：

DUALITY; INVEXITY;

D O I：

10.1155/2014/317304

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are interested in a nonsmooth minimax programming Problem (SIP). Firstly, we establish the necessary optimality conditions theorems for Problem (SIP) when using the well-known Caratheodory's theorem. Under the Lipschitz (Phi, rho)-invexity assumptions, we derive the sufficiency of the necessary optimality conditions for the same problem. We also formulate dual and establish weak, strong, and strict converse duality theorems for Problem (SIP) and its dual. These results extend several known results to a wider class of problems.

引用

页数：7

共 22 条

[1]

Ahmad I., 2011, J INEQUALITIES APPL, V2011

[2]

[Anonymous], 2009, Encyclopedia of Optimization

[3] THE NOTION OF V-r-INVEXITY IN DIFFERENTIABLE MULTIOBJECTIVE PROGRAMMING [J].

Antczak, T. .

JOURNAL OF APPLIED ANALYSIS, 2005, 11 (01) :63-79

[4] Minimax programming under (p,r)-invexity [J].

Antczak, T .

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2004, 158 (01) :1-19

[5]

Antczak T., 2001, J MATH ANAL APPL, V80, P545

[6] Generalized fractional minimax programming with B-(p, r)-invexity [J].

Antczak, Tadeusz .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (06) :1505-1525

[7] Nonsmooth minimax programming under locally Lipschitz (Φ, ρ)-invexity [J].

Antczak, Tadeusz .

APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (23) :9606-9624

[8] (Φ,π)-Invexity in Nonsmooth Optimization [J].

Antczak, Tadeusz ;

Stasiak, Aleksandra .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2011, 32 (01) :1-25

[9] WHAT IS INVEXITY [J].

BENISRAEL, A ;

MOND, B .

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES B-APPLIED MATHEMATICS, 1986, 28 :1-9

[10]

Caristi G, 2006, LECT NOTES ECON MATH, V583, P167

← 1 2 3 →