Hybrid approach for solving multiple-objective linear programs in outcome space
Journal of Optimization Theory and Applications
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Multicriteria Optimization
An Algorithm for Approximating Convex Pareto Surfaces Based on Dual Techniques
INFORMS Journal on Computing
An objective space cut and bound algorithm for convex multiplicative programmes
Journal of Global Optimization
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In multi-objective convex optimization it is necessary to compute an infinite set of nondominated points. We propose a method for approximating the nondominated set of a multi-objective nonlinear programming problem, where the objective functions and the feasible set are convex. This method is an extension of Benson's outer approximation algorithm for multi-objective linear programming problems. We prove that this method provides a set of weakly 驴-nondominated points. For the case that the objectives and constraints are differentiable, we describe an efficient way to carry out the main step of the algorithm, the construction of a hyperplane separating an exterior point from the feasible set in objective space. We provide examples that show that this cannot always be done in the same way in the case of non-differentiable objectives or constraints.