A feasible direction algorithm for nonlinear second-order cone programs

Alfredo Canelas, Miguel Carrasco, Julio López

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this work, we present a new feasible direction algorithm for solving smooth nonlinear second-order cone programs. These consist of minimizing a nonlinear smooth objective function subject to some nonlinear second-order cone constraints. Given an interior point to the feasible set defined by the conic constraints, the algorithm generates a feasible sequence with monotone decreasing values of the objective function. Under mild assumptions, we prove the global convergence of the algorithm to KKT points. Finally, we present some computational results applied to several instances of randomly generated benchmark problems and robust support vector machine classification.
Original languageAmerican English
Pages (from-to)1322-1341
Number of pages20
JournalOptimization Methods and Software
Volume34
Issue number6
DOIs
StatePublished - 2 Nov 2019

Keywords

  • 49M15
  • 90C30
  • 90C51
  • Feasible direction
  • Interior-point methods
  • Second-order cone programming

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