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Transformation or penalty function techniques have enjoyed wide popularity for the solution of nonlinear programming problems in recent years. Many methods have been proposed in this class, including the Method of Multipliers. In this paper we present two enhancements which may be used with any transformation technique. The first is a technique for direct handling of variable bounds, and the second is a problem scaling algorithm. Both techniques have been implemented in connection with a Method of Multipliers code, BIAS, and applied to 23 test problems. The numerical results indicate a significant increase in the robustness and overall efficiency of the transformation method employed.

A new method of generating solutions for the matrix method of linkage analysis is considered. Optimization techniques are used to close the matrix loop equations iteratively until they are sufficiently close to closure to allow a solution by Newton’s method. The method is especially applicable for generating the initial closed position of a general three-dimensional mechanism. This technique is demonstrated on several three-dimensional mechanism examples.

This paper presents Schuldt’s Method of Multipliers for nonlinear programming problems. The basics of this new exterior penalty function method are discussed with emphasis upon the ease of implementation. The merit of the technique for medium to large non-linear programming problems is evaluated, and demonstrated using the Eason and Fenton test problems.

A complete survey of the application of optimization techniques to the design of mechanisms is given. The survey begins with the work of Da Vinci, Newton, and Chebychev and progresses to the most contemporary contributors including Freudenstein, Tomas, Siddall, Fox, Gupta, and Tesar. An effort is made to be complete and to show the complimentary development of the two important fields of optimization and mechanism synthesis.