Constrained Nonlinear Optimization by Heuristic Programming

D. A. Paviani and D. M. Himmelblau
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D. A. Paviani: The University of Texas, Austin, Texas
D. M. Himmelblau: The University of Texas, Austin, Texas

Operations Research, 1969, vol. 17, issue 5, 872-882

Abstract: This paper develops a new algorithm for solving the general nonlinear programming problem that melds the flexible simplex search of Nelder and Mead with various additional rules to take care of equality and/or inequality constraints. The set of violated inequalities and equalities is lumped into one inequality constraint loosely satisfied during the early progress of the optimization and more closely satisfied during its final stages. To permit this type of search, the method sets up a special tolerance criterion, a function that does not depend on either the values of the objective function or the values of the constraints. The new algorithm has solved successfully a number of problems that have been proposed in the literature as test problems. Finally, to indicate the algorithm's capabilities, the paper describes an example composed of a linear objective function of twenty-four variables subject to fourteen nonlinear equalities and thirty inequalities.

Date: 1969
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