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Optimality conditions for nonlinear second-order cone programming and symmetric cone programming

Roberto Andreani (andreani***at***ime.usp.br)
Ellen H. Fukuda (ellen***at***i.kyoto-u.ac.jp)
Gabriel Haeser (ghaeser***at***ime.usp.br)
Daiana O. Santos (daiana***at***ime.usp.br)
Leonardo D. Secchin (leonardo.secchin***at***ufes.br)

Abstract: Nonlinear symmetric cone programming (NSCP) generalizes important optimization problems such as nonlinear programming, nonlinear semidefinite 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 better global convergence results.

Keywords: second-order cones, symmetric cones, optimality conditions, constraint qualifications, augmented Lagrangian method

Category 1: Nonlinear Optimization

Category 2: Linear, Cone and Semidefinite Programming

Category 3: Linear, Cone and Semidefinite Programming (Second-Order Cone Programming )


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Entry Submitted: 10/16/2019
Entry Accepted: 10/16/2019
Entry Last Modified: 10/17/2019

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