A finite nonadjacent extreme-point search algorithm for optimization over the efficient set
Journal of Optimization Theory and Applications
Optimizing a linear function over an efficient set
Journal of Optimization Theory and Applications
Journal of Optimization Theory and Applications
An Inner Approximation Method for Optimization over the Weakly Efficient Set
Journal of Global Optimization
Conical Algorithm in Global Optimization for Optimizing over Efficient Sets
Journal of Global Optimization
Optimization over the efficient set: overview
Journal of Global Optimization
Robust Solution of Nonconvex Global Optimization Problems
Journal of Global Optimization
Multicriteria Optimization
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This article presents for the first time an algorithm specifically designed for globally minimizing a finite, convex function over the weakly efficient set of a multiple objective nonlinear programming problem (V1) that has both nonlinear objective functions and a convex, nonpolyhedral feasible region. The algorithm uses a branch and bound search in the outcome space of problem (V1), rather than in the decision space of the problem, to find a global optimal solution. Since the dimension of the outcome space is usually much smaller than the dimension of the decision space, often by one or more orders of magnitude, this approach can be expected to considerably shorten the search. In addition, the algorithm can be easily modified to obtain an approximate global optimal weakly efficient solution after a finite number of iterations. Furthermore, all of the subproblems that the algorithm must solve can be easily solved, since they are all convex programming problems. The key, and sometimes quite interesting, convergence properties of the algorithm are proven, and an example problem is solved.