Optimality Conditions for Nonlinear Second-Order Cone Programming and Symmetric Cone Programming

Roberto Andreani, Ellen H. Fukuda, Gabriel Haeser (), Daiana O. Santos and Leonardo D. Secchin
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Roberto Andreani: University of Campinas
Ellen H. Fukuda: Kyoto University
Gabriel Haeser: University of São Paulo
Daiana O. Santos: Federal University of São Paulo
Leonardo D. Secchin: Federal University of Espírito Santo

Journal of Optimization Theory and Applications, 2024, vol. 200, issue 1, No 1, 33 pages

Abstract: Abstract Nonlinear symmetric cone programming (NSCP) generalizes important optimization problems such as nonlinear programming, nonlinear semi-definite programming and nonlinear second-order cone programming (NSOCP). In this work, we present two new optimality conditions for NSCP without constraint qualifications, which implies the Karush–Kuhn–Tucker conditions under a condition weaker than Robinson’s constraint qualification. In addition, we show the relationship of both optimality conditions in the context of NSOCP, where we also present an augmented Lagrangian method with global convergence to a KKT point under a condition weaker than Robinson’s constraint qualification.

Keywords: Second-order cones; Symmetric cones; Optimality conditions; Constraint qualifications; Augmented Lagrangian method (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-023-02338-6

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