On Approximate Vector Optimization

Valyi, I. (1986). On Approximate Vector Optimization. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-86-007

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Abstract

The roots of current interest in the theory of approximate solutions of optimization problems lie in approximation theory and nondifferentiable optimization. In this paper an approximate saddle point theory is presented for vector valued convex optimization problems. The considerations cover different possible types of approximate optimality, including both the efficient, or Pareto-type, which is more frequently used in practical decision making applications, and the absolute, or strict type, which is more of theoretical interest. The saddle point theorems are used to study duality in the context of approximate solutions. The approach of the paper also provides for a unified view of a number of results achieved either in approximate scalar optimization or exact vector optimization.

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