A Symmetric Duality Concept for Linear Goal Programming: Principal Results (original) (raw)

A symmetric duality concept for linear goal programming

Linear goal programming (GP) is a widely used tool for dealing with problems involving multiple objectives. This paper aims to introduce a new concept of duality for GP. In this concept the dual to a minsum GP problem is a GP problem and the dual to a lexicographic GP problem is a multidimensional lexicographic GP problem. We prove most of typical dual relations including the saddle-point property and the formula for marginal values.

Symmetric duality theory for linear goal programming

Optimization, 1988

Sumrnary: Linear goal progra,mming (GP) is a widely used tool for dealing with problems involving multiplo objectives. This paper" aims to develope a new concept of duality for GP. In this concepl, the dual to a minsumGP problem is a GP ploblem and the dual to a, lexicographic GP problem is a multidimensional lexicographic GP problem. 14re prove most, of the typical dual relations including the saddle-point ploperty ancl the formula for marginal values.

Symmetric Duality in Multi – Objective Programming

International Journal of Mathematics Trends and Technology, 2016

Dorn introduced symmetric duality in nonlinear programming by defining a program and it’s dual to be symmetric if the dual of the dual is the original problem. In the past, the symmetric duality has been studied extensively in the literature by Dantzig and Mond and Weir. Recently, Weit and Mond studied symmetric duality in the context of multi-objective programming by introducing a multi-objective analogue of the primal-dual pair presented in Mond. Although the multi-objective primal dual pair constructed in subsumes the single objective symmetric duality as a special case, the construction of seems to be somewhat restricted because the same parameter p R   (vector multiplier corresponding to various objectives) is present in both primal and dual. Further, the proof of the main duality result assumes this  to be fixed in the dual problem. The main aim of this paper is to present a pair of multi-objective programming problem (P) and Duality (D) with  as variable in both programs ...

Second Order Duality in Multiobjective Programming

Journal of Applied Analysis, 2008

A nonlinear multiobjective programming problem is considered. Weak, strong and strict converse duality theorems are established under generalized second order (F, α, ρ, d)-convexity for second order Mangasarian type and general Mond-Weir type vector duals.

Duality in Multiobjective Optimization Problems with Set Constraints

We propose four different duality problems for a vector optimization program with a set constraint, equality and inequality constraints. For all dual problems we state weak and strong duality theorems based on different generalized concavity assumptions. The proposed dual problems provide a unified framework generalizing Wolfe and Mond-Weir results.

A general correspondence between dual minimax problems and convex programs

Pacific Journal of Mathematics, 1968

The Kuhn-Tucker theory of Lagrange multipliers centers on a one-to-one correspondence between nonlinear programs and minimax problems. This correspondence has been extended by Dantzig, Eisenberg and Cottle to one in which every minimax problem of a certain type gives rise to a pair of nonlinear programs dual to each other. The aim here is to show how, by forming conjugates of convex functions and saddlefunctions (i.e. functions of two vector arguments which are convex in one argument and concave in the other), one can set up a more symmetric correspondence with even stronger duality properties. The correspondence concerns problems in quartets, each quartet being comprised of a dual pair of convex and concave programs and a dual pair of minimax problems. The whole quartet can be generated directly from any one of its members.

Second-order symmetric duality in multiobjective programming

Applied Mathematics Letters, 2001

pair of second-order symmetric dual models for multiobJective nonlinear programmmg 1s proposed m this paper We prove the weak, strong, and converse duality theorems for the formulated second-order symmetric dual programs under mvexity condltlons

Duality in Optimization and Constraint Satisfaction

2006

We show that various duals that occur in optimization and constraint satisfaction can be classified as inference duals, relaxation duals, or both. We discuss linear programming, surrogate, Lagrangean, superadditive, and constraint duals, as well as duals defined by resolu- tion and filtering algorithms. Inference duals give rise to nogood-based search methods and sensitivity analysis, while relaxation duals provide bounds. This