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A Penalty-Interior-Point Algorithm for Nonlinear Constrained Optimization

Frank E. Curtis (frank.e.curtis***at***gmail.com)

Abstract: Penalty and interior-point methods for nonlinear optimization problems have enjoyed great successes for decades. Penalty methods have proved to be effective for a variety of problem classes due to their regularization effects on the constraints. They have also been shown to allow for rapid infeasibility detection. Interior-point methods have become the workhorse in large-scale optimization due to their Newton-like qualities, both in terms of their scalability and convergence behavior. Each of these two strategies, however, have certain disadvantages that make their use either impractical or inefficient for certain classes of problems. The goal of this paper is to present a penalty-interior-point method that possesses the advantages of penalty and interior-point techniques, but does not suffer from their disadvantages. Numerous attempts have been made along these lines in recent years, each with varying degrees of success. The novel feature of the algorithm in this paper is that our focus is not only on the formulation of the penalty-interior-point subproblem itself, but on the design of updates for the penalty and interior-point parameters. The updates we propose are designed so that rapid convergence to a solution of the nonlinear optimization problem or an infeasible stationary point is attained. We motivate the convergence properties of our algorithm and illustrate its practical performance on large sets of problems, including sets of problems that exhibit degeneracy or are infeasible.

Keywords: nonlinear optimization, large-scale optimization, nonconvex optimization, constrained optimization, penalty methods, interior-point methods, penalty-interior-point methods

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: F. E. Curtis, “A Penalty-Interior-Point Algorithm for Nonlinear Constrained Optimization,” Mathematical Programming Computation, 4(2): 181–209, 2012.

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Entry Submitted: 06/21/2010
Entry Accepted: 06/21/2010
Entry Last Modified: 01/04/2013

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