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A primal-dual modified log-barrier method for inequality constrained nonlinear optimization

Joshua Griffin (joshua.griffin***at***sas.com)
Riadh Omheni (riadh.omheni***at***sas.com)

Abstract: We present a primal-dual modified log-barrier algorithm to solve inequality constrained nonlinear optimization problems. Basically, the algorithm is a Newton-like method applied to a perturbation of the optimality system that follows from a reformulation of the initial problem by introducing a modified log-barrier function to handle inequality constraints. The algorithm uses an outer/inner iteration scheme and the globalization is performed in the primal-dual space by means of a new primal-dual merit function. The robustness and efficiency of the algorithm is improved using quadratic extrapolation. The numerical performance of the new method is illustrated by comparing it with a primal-dual classical log-barrier method and two well-established interior-point solvers on two sets of problems from COPS and Hock-Schittkowski collections, including a set of problems that exhibits degeneracy.

Keywords: Nonlinear programming, Inequality constrained optimization, Modified log-barrier method, Primal-dual method, Numerical tests

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )


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Entry Submitted: 01/29/2020
Entry Accepted: 01/29/2020
Entry Last Modified: 03/09/2020

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