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Derivative-free methods for constrained mixed-integer optimization

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

Abstract: We consider the problem of minimizing a continuously di erentiable function of several variables subject to simple bound and general nonlinear inequality constraints, where some of the variables are restricted to take integer values. We assume that the rst order derivatives of the objective and constraint functions can be neither calculated nor approximated explicitly. This class of mixed integer nonlinear optimization problems arises frequently in many industrial and scienti c applications and this motivates the increasing interest in the study of derivative-free methods for their solution. The continuous variables are handled by a linesearch strategy whereas to tackle the discrete ones we employ a local search-type approach. Nonlinear constraints are handled by using a quadratic penalty function approach. We propose two algorithms which are characterized by the way the current iterate is updated and by the stationarity conditions satis ed by the limit points of the sequences they produce. We report a computational experience both on standard test problems and on a realoptimal design problem. We also compare the performances of the proposed methods with those of a well-known derivative-free optimization software package, i.e. NOMAD.

Keywords: Mixed-integer nonlinear programming, derivative-free optimization, nonlinear constrained optimization.

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Report IASI R11.11

Download: [Postscript][PDF]

Entry Submitted: 10/03/2011
Entry Accepted: 10/03/2011
Entry Last Modified: 11/15/2013

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