Optimization Online


Exact augmented Lagrangian functions for nonlinear semidefinite programming

Ellen H. Fukuda (ellen***at***i.kyoto-u.ac.jp)
Bruno F. Lourenco (lourenco***at***mist.i.u-tokyo.ac.jp)

Abstract: In this paper, we study augmented Lagrangian functions for nonlinear semidefinite programming (NSDP) problems with exactness properties. The term exact is used in the sense that the penalty parameter can be taken appropriately, so a single minimization of the augmented Lagrangian recovers a solution of the original problem. This leads to reformulations of NSDP problems into unconstrained nonlinear programming ones. Here, we first establish a unified framework for constructing these exact functions, generalizing Di Pillo and Lucidi's work from 1996, that was aimed at solving nonlinear programming problems. Then, through our framework, we propose a practical augmented Lagrangian function for NSDP, proving that it is continuously differentiable and exact under the so-called nondegeneracy condition. We also present some preliminary numerical experiments.

Keywords: Differentiable exact merit functions, generalized augmented Lagrangian functions, nonlinear semidefinite programming

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Kyoto University and Seikei University, May/2017

Download: [PDF]

Entry Submitted: 05/18/2017
Entry Accepted: 05/18/2017
Entry Last Modified: 06/20/2018

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society