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A Feasible Direction Algorithm for Nonlinear Second-Order Cone Optimization Problems

Alfredo Canelas(acanelas***at***i ng.edu.uy)
Miguel Carrasco(micarrasco***at***uandes.cl)
Julio López(julio.lopez***at***udp.cl)

Abstract: In this work we present a new feasible direction algorithm for solving smooth nonlinear second-order cone programs. These problems consist of minimizing a nonlinear di erentiable objective function subject to some nonlinear second-order cone constraints. Given a point interior to the feasible set de nfined by the nonlinear constraints, the proposed approach computes a feasible and descent direction for the objective function. The search direction is computed by using a formulation that is similar to the algorithm FDIPA for nonlinear programming. A line search along the search direction fi nds a new feasible point that has a lower value of the objective function. Repeating this process, the algorithm generates a feasible sequence with a monotone decrease of the objective function. Under mild assumptions we prove that the present algorithm converge globally to stationary points of the nonlinear second-order cone program. We test our algorithm with several instances of robust classi cation of support vector machines.

Keywords: Feasible direction, second-order cone programming, interior point algorithm, support vector machines

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Global Optimization (Applications )

Citation: Alfredo Canelas, Instituto de Estructuras y Transporte, Facultad de Ingeniería, Universidad de la República, Montevideo, Uruguay. Miguel Carrasco, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Santiago, Chile. Julio Lopez, Facultad de Ingeniería, Universidad Diego Portales, Santiago, Chile.

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Entry Submitted: 08/21/2014
Entry Accepted: 08/21/2014
Entry Last Modified: 08/21/2014

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