New strong duality results for convex programs with separable constraints

We introduce a higher-order duality (Mangasarian type and Mond-Weir type) for the control problem. Under the higher-order generalized invexity assumptions on the functions that compose the primal problems, higher-order duality results (weak duality, strong duality, and converse duality) are derived for these pair of problems. Also, we establish few examples in support of our investigation.

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Higher order duality for cone vector optimization problems

Asian-European Journal of Mathematics ◽

10.1142/s1793557120500205 ◽

2018 ◽

Vol 13 (01) ◽

pp. 2050020

Author(s):

Vivek Singh ◽

Anurag Jayswal ◽

S. Al-Homidan ◽

I. Ahmad

Keyword(s):

Vector Optimization ◽

Optimization Problems ◽

Strong Duality ◽

Vector Optimization Problem ◽

Higher Order ◽

Support Functions ◽

Invex Functions ◽

New Class ◽

Duality Results ◽

Higher Order Duality

In this paper, we present a new class of higher order [Formula: see text]-[Formula: see text]-invex functions over cones. Further, we formulate two types of higher order dual models for a vector optimization problem over cones containing support functions in objectives as well as in constraints and establish several duality results, viz., weak and strong duality results.

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CONE CONVEX AND RELATED FUNCTIONS IN OPTIMIZATION OVER TOPOLOGICAL VECTOR SPACES

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595907001504 ◽

2007 ◽

Vol 24 (06) ◽

pp. 741-754

Author(s):

S. K. SUNEJA ◽

MEETU BHATIA

Keyword(s):

Optimality Conditions ◽

Minimization Problem ◽

Convex Functions ◽

Strong Duality ◽

Vector Spaces ◽

Sufficient Optimality Conditions ◽

Topological Vector Spaces ◽

Duality Results ◽

Gateaux Derivatives ◽

Vector Valued

In this paper cone convex and related functions have been studied. The concept of cone semistrictly convex functions on topological vector spaces is introduced as a generalization of semistrictly convex functions. Certain properties of these functions have been established and their interrelations with cone convex and cone subconvex functions have been explored. Assuming the functions to be cone subconvex, sufficient optimality conditions are proved for a vector valued minimization problem over topological vector spaces, involving Gâteaux derivatives. A Mond-Weir type dual is associated and weak and strong duality results are proved.

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Strong Duality and Optimality Conditions for Generalized Equilibrium Problems

Abstract and Applied Analysis ◽

10.1155/2013/176363 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8

Author(s):

D. H. Fang ◽

J. F. Bao

Keyword(s):

Optimality Conditions ◽

Equilibrium Problem ◽

Equilibrium Problems ◽

Necessary Conditions ◽

Strong Duality ◽

Conjugate Functions ◽

Generalized Equilibrium Problem ◽

Dc Functions ◽

Duality Results ◽

Generalized Equilibrium

We consider a generalized equilibrium problem involving DC functions. By using the properties of the epigraph of the conjugate functions, some sufficient and/or necessary conditions for the weak and strong duality results and optimality conditions for generalized equilibrium problems are provided.

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Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related Functions

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2014/496149 ◽

2014 ◽

Vol 2014 ◽

pp. 1-12 ◽

Cited By ~ 3

Author(s):

Hachem Slimani ◽

Shashi Kant Mishra

Keyword(s):

Fractional Programming ◽

Inequality Constraints ◽

Strong Duality ◽

Multiple Objective ◽

Type I ◽

Multiobjective Fractional Programming ◽

Duality Results ◽

Preinvex Functions ◽

Necessary And Sufficient ◽

Efficiency Conditions

We study a nonlinear multiple objective fractional programming with inequality constraints where each component of functions occurring in the problem is considered semidifferentiable along its own direction instead of the same direction. New Fritz John type necessary and Karush-Kuhn-Tucker type necessary and sufficient efficiency conditions are obtained for a feasible point to be weakly efficient or efficient. Furthermore, a general Mond-Weir dual is formulated and weak and strong duality results are proved using concepts of generalized semilocally V-type I-preinvex functions. This contribution extends earlier results of Preda (2003), Mishra et al. (2005), Niculescu (2007), and Mishra and Rautela (2009), and generalizes results obtained in the literature on this topic.

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Some results on symmetric duality of mathematical fractional programming with generalized $F$-convexity complex spaces

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.36.2005.128 ◽

2005 ◽

Vol 36 (2) ◽

pp. 159-165

Author(s):

Deo Brat Ojha

Keyword(s):

Fractional Programming ◽

General Type ◽

Strong Duality ◽

Objective Functions ◽

Symmetric Duality ◽

Support Functions ◽

Complex Spaces ◽

Duality Results ◽

Special Cases ◽

Convexity Assumptions

In this present article we have given some mathematical fractional programming problems with their symmetric duals and have derived weak and strong duality results with respect to such programs. Moreover, we have also used most general type of convexity assumptions involved with the functions which are related to the programming problems. It is to be pointed out that the objective functions in such programs contain terms like support functions which in turn are able to give results on particular classes of programs involving quadratic terms. Our results in particular give as of special cases some eariler results symmetric duals given in the current literature. All discussion goes to complex spaces.

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Efficiency and duality in nonsmooth multiobjective fractional programming involving η-pseudolinear functions

Yugoslav journal of operations research ◽

10.2298/yjor101215002m ◽

2012 ◽

Vol 22 (1) ◽

pp. 3-18 ◽

Cited By ~ 3

Author(s):

S.K. Mishra ◽

B.B. Upadhyay

Keyword(s):

Fractional Programming ◽

Dual Problem ◽

Feasible Solution ◽

Strong Duality ◽

Sufficient Optimality Conditions ◽

Boundedness Condition ◽

Multiobjective Fractional Programming ◽

Duality Results ◽

Multiobjective Fractional Programming Problem ◽

Necessary And Sufficient

In this paper, we shall establish necessary and sufficient optimality conditions for a feasible solution to be efficient for a nonsmooth multiobjective fractional programming problem involving ?-pseudolinear functions. Furthermore, we shall show equivalence between efficiency and proper efficiency under certain boundedness condition. We have also obtained weak and strong duality results for corresponding Mond-Weir subgradient type dual problem. These results extend some earlier results on efficiency and duality to multiobjective fractional programming problems involving ?-pseudolinear and pseudolinear functions.

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