A penalty-interior-point algorithm for nonlinear constrained optimization |
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Authors: | Frank E Curtis |
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Institution: | 1.Department of Industrial and Systems Engineering,Lehigh University,Bethlehem,USA |
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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. |
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Keywords: | |
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