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The solution of Euclidean norm trust region SQP subproblems via second order cone programs, an overview and elementary introduction

Florian Jarre (jarre***at***hhu.de)
Felix Lieder (felix.lieder***at***hhu.de)

Abstract: It is well known that convex SQP subproblems with a Euclidean norm trust region constraint can be reduced to second order cone programs for which the theory of Euclidean Jordan-algebras leads to efficient interior-point algorithms. Here, a brief and self-contained outline of the principles of such an implementation is given. All identities relevant for the implementation are derived from scratch and are compared to interior-point methods for linear programs. Sparsity of the data of the SQP subproblem can be maintained essentially in the same way as for interior-point methods for linear programs. The presentation is intended as an introduction for students and for colleagues who may have heard about Jordan algebras but did not yet find the time to get involved with them. A simple Matlab implementation is made available and the discussion of implementational aspects addresses a scaling property that is critical for SQP subproblems.

Keywords: Second order cone program, Jordan algebra, SQP subproblem.

Category 1: Linear, Cone and Semidefinite Programming (Second-Order Cone Programming )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: To appear in: Optimization Methods and Software 2017

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Entry Submitted: 08/21/2015
Entry Accepted: 08/21/2015
Entry Last Modified: 01/03/2017

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