B. Mond

Pre-invex functions in multiple objective optimization

and called such functions convexlike. If S is a convex set and if f is a convex function, then clearly f is convexlike. Elster and Nehse obtained a saddlepoint optimality condition for convexlike mathematical programs. Hayashi and Komiya [9] also considered convexlike functions and developed a Gordan-type theorem of the alternative involving convexlike functions and in addition considered Lagrangian duality for convexlike programs. Hanson [7] considered differentiable functions f: S + R for which there exists an n-dimensional vector function q(,q U) such that for all x, u E S

Generalised convexity and duality in multiple objective programming

By considering the concept of weak minima, different scalar duality results are extended to multiple objective programming problems. A number of weak, strong and converse duality theorems are given under a variety of generalised convexity conditions.

Duality and sufficiency in control problems with invexity

Recently, Mond, Chandra, and Husain [3] established duality results for a variational problem under more general convexity conditions, called invex, than Mond and Hanson [4]. In a similar fashion, the results of Mond and Hanson [S] for duality in control problems are extended to more general convex, or invex, functions. It is also shown that for invex functions, the necessary conditions for optimality in the control problem are also sufficient.

Generalized fractional programming duality: a ratio game approach

A ratio game approach to the generalized fractional programming problem is presented and duality relations established. This approach suggests certain solution procedures for solving fractional programs involving several ratios in the objective function.

Symmetric Dual Fractional Programming

A pair of symmetric dual fractional programming problems is formulated and appropriate duality theorems are established.ZusammenfassungEs wird ein symmetrisches Paar primaler und dualer Quotientenprogramme eingeführt, für das Dualitätsbeziehungen hergeleitet werden.

Generalized concavity and duality with a square root term

Duality results for a class of nondifferentiable mathematical programming problems are given. These results allow for the weakening of the usual convexity conditions required for duality to hold. A pair of symmetric and self dual nondifferentiable programs under weaker convexity conditions are also given. A subgradient symmetric duality is proposed and its limitations discussed. Finally, a pair of nondifferentiable mathematical programs containing arbitrary norms is presented.

Vector-valued lagrangian and multiobjective fractional programming duality

A class of multiobjective fractional programming problems is considered and duality results are established in terms of properly efficient solutions of the primal and dual programs. Further a vector-valued ratio type Lagrangian is introduced and certain vector saddlepoint results are presented.

Weak minimization and duality

Sufficient and necessary optimality conditions are given for weakly minimized optimization problems in terms of a vector valued Lagrangian. Lagrangian and Wolfe type duals are constructed and duality established using an ordering that accords with the definition of a weak minimum. The results for differentiable problems continue to hold under weakened convexity assumptions and for problems which quasiminimize rather than minimize.

Transposition Theorems for Cone-Convex Functions

Some transposition theorems for real convex functions on real finite-dimensional spaces, with inequality ordering, are extended to convex functions mapping real Banach spaces into Banach spaces, with partial orderings and convexity defined by closed convex cones.Applications to optimization and optimal control are discussed.

The Dual of a Fractional Linear Program

Abstract A linear fractional program is shown, under certain restrictions, to have a fractional linear program as its dual.