On interval-valued optimization problems with generalized invex functions

This paper is devoted to study interval-valued optimization problems. Sufficient optimality conditions are established for LU optimal solution concept under generalized (p,r)−ρ−(η,θ)-invexity. Weak, strong and strict converse duality theorems for Wolfe and Mond-Weir type duals are derived in order to relate the LU optimal solutions of primal and dual problems.MSC: 90C46, 90C26, 90C30.

[1]  Laisheng Wang,et al.  Optimality conditions and duality in nondifferentiable interval-valued programming , 2012 .

[2]  P. Mandal,et al.  Symmetric duality with (p, r) - ρ - (η, θ)-invexity , 2011, Appl. Math. Comput..

[3]  M. A. Hanson.  On sufficiency of the Kuhn-Tucker conditions , 1981 .

[4]  Raymond Nadeau,et al.  An Interactive Method To Multiobjective Linear Programming Problems With Interval Coefficients , 1992 .

[5]  Ajay Kumar Bhurjee,et al.  Efficient solution of interval optimization problem , 2012, Math. Methods Oper. Res..

[6]  S. Chanas,et al.  Multiobjective programming in optimization of interval objective functions -- A generalized approach , 1996 .

[7]  Lifeng Li,et al.  The KKT optimality conditions in a class of generalized convex optimization problems with an interval-valued objective function , 2014, Optim. Lett..

[8]  Generalized sufficiency criteria in continuous-time programming with application to a class of variational-type inequalities , 1990 .

[9]  Alexander Rubinov,et al.  𝔹-Convex Sets and Functions , 2006 .

[10]  Hsien-Chung Wu.  Duality Theory for Optimization Problems with Interval-Valued Objective Functions , 2010 .

[11]  Yi-Ju Wang,et al.  Optimality Condition and Mixed Duality for Interval-Valued Optimization , 2009, ICFIE.

[12]  Andreas Prekopa,et al.  Stochastic programming with multiple objective functions: I.M. STANCU-MINASIAN Mathematics and Its Applications (East European Series), Reidel, Dordrecht, 1984, xiv + 334 pages, Dfl.160.00 , 1986 .

[13]  Tadeusz Antczak,et al.  (p, r)-Invex Sets and Functions☆ , 2001 .

[14]  R. Słowiński,et al.  Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty , 1990, Theory and Decision Library.

[15]  I. M. Stancu-Minasian,et al.  Stochastic Programming: with Multiple Objective Functions , 1985 .

[16]  Hsien-Chung Wu.  On interval-valued nonlinear programming problems , 2008 .

[17]  I. M. Stancu-Minasian,et al.  Multiobjective Mathematical Programming with Inexact Data , 1990 .

[18]  Abraham Charnes,et al.  An Algorithm for Solving Interval Linear Programming Problems , 1977, Oper. Res..

[19]  Hsien-Chung Wu.  Wolfe Duality for Interval-Valued Optimization , 2008 .

[20]  Hsien-Chung Wu,et al.  The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function , 2007, Eur. J. Oper. Res..

[21]  Izhar Ahmad,et al.  On sufficiency and duality for a class of interval-valued programming problems , 2011, Appl. Math. Comput..

[22]  Bing-yuan Cao,et al.  Fuzzy Information and Engineering Volume 2 , 2009 .

[23]  Ralph E. Steuer.  Algorithms for Linear Programming Problems with Interval Objective Function Coefficients , 1981, Math. Oper. Res..