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A DERIVATIVE-FREE APPROACH TO CONSTRAINED MULTIOBJECTIVE NONSMOOTH OPTIMIZATION

Giampaolo Liuzzi(giampaolo.liuzzi***at***iasi.cnr.it)
Stefano Lucidi(lucidi***at***dis.uniroma1.it)
Francesco Rinaldi(rinaldi***at***math.unipd.it)

Abstract: In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box. We define a linesearch-based solution method, and we show that it converges to a set of Pareto stationary points. To this aim, we carry out a theoretical analysis of the problem by only assuming Lipschitz continuity of the functions; more specifically, we give new optimality conditions that take explicitly into account the bound constraints, and prove that the original problem is equivalent to a bound constrained problem obtained by penalizing the nonlinear constraints with an exact merit function. Finally, we present the results of a numerical experimentation on bound constrained and nonlinearly constrained problems, showing that our approach is promising when compared to a state-of-the-art method from the literature.

Keywords: Derivative-free multiobjective optimization, Lipschitz optimization, Inequality constraints, Exact penalty functions

Category 1: Nonlinear Optimization

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation:

Download: [Postscript][PDF]

Entry Submitted: 07/29/2015
Entry Accepted: 07/29/2015
Entry Last Modified: 07/29/2015

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