A feasible direction algorithm for nonlinear second-order cone programs

Alfredo Canelas, Miguel Carrasco*, Julio López

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 languageEnglish
Pages (from-to)1322-1341
Number of pages20
JournalOptimization Methods and Software
Issue number6
StatePublished - 2 Nov 2019

Bibliographical note

Funding Information:
The first author was supported by the Uruguayan Councils Agencia Nacional de Investigaci?n e Innovaci?n (ANII) and Comisi?n Sectorial de Investigaci?n Cient?fica (CSIC). The second author was supported by Fondo Nacional de Desarrollo Cient?fico y Tecnol?gico (FONDECYT) grant number 1130905. The third author was supported by FONDECYT grant number 1160894. The authors would like to thank the anonymous reviewers for their valuable comments and suggestions.

Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.


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


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