Implementation of an Exact Penalty Function Formulation to Solve Convex Nonlinear Programming Problems
RENSSELAER POLYTECHNIC INST TROY NY DEPT OF MATHEMATICAL SCIENCES
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A convex nonlinear programming problem NLP can be reformulated using an exact penalty function. One such function is the L1 exact penalty function examined by Zangwill. The result of this reformulation is an unconstrained optimization problem. Unfortunately, this nonlinear, convex function is not a continuously differentiable function. Most computer methods algorithms are based on the condition that the functions involved are differentiable. One exception is the Ellipsoid Algorithm, EA3, by Ecker and Kupferschmid. This algorithm, while demonstrating only linear convergence, has been shown to be robust in solving problems with nondifferentiable functions. The problem reduces to the following question. Is it better to solve the original, constrainted problem, or the reformulated unconstrained problem Here, better is defined as faster and more accurate. After demonstrating that the exact penalty formulation will always solve the convex NLP, comparison are made, using the ellipsoid algorithm, of accuracy of solution and solution time for several example problems.
- Operations Research