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Optimization over the Efficient Set of a Bicriteria Convex Programming Problem

Thi Bach Kim NGUYEN (kimntb-fami***at***mail.hut.edu.vn)
Ngoc Thang TRAN (thangtn-fami***at***mail.hut.edu.vn)

Abstract: The problem of optimizing a real function over the efficient set of a multiple objective programming problem arises in a variety of applications. In this article, we propose an outer approximation algorithm for maximizing a function $h(x) = \varphi(f(x))$ over the efficient set $X_E$ of the bi-criteria convex programming problem $ {\rm Vmin} \{f(x)=(f_1(x), f_2(x))^T | x \in X \}$, where $\varphi$ is an increasing function on $f(X)$. The convergence of the algorithm is established. To illustrate the new algorithm, we apply it to the solution of the sample problem. Preliminary computational results with the proposed algorithm are reported.

Keywords: Global optimization, Optimization over the efficient set, Outcome set, Bicriteria convex programming, Outer approximation, Branch-and-reduce scheme

Category 1: Global Optimization

Category 2: Nonlinear Optimization

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Entry Submitted: 10/06/2011
Entry Accepted: 10/07/2011
Entry Last Modified: 02/21/2012

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