Optimization over the E-cient Set of a Bicriteria Convex Programming Problem ⁄
Nguyen Thi Bach Kim, Tran Ngoc Thang · 2011
The problem of optimizing a real function over the e‐cient 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) = ’(f(x)) over the e‐cient set XE of the bi-criteria convex programming problem Vminff(x) = (f1(x);f2(x)) T jx 2 Xg, where ’ 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. AMS Subject Classiflcation: 2000 Mathematics Subject Classiflcation. Primary: 90 C29; Secondary: 90 C26