Abstract. We discuss an algorithm for the numerical solution of the Obstacle Problem in which the coincidence set is considered as the prime unknown. Domain functionals are defined for which the coincidence set serves as the minimizing element. Their gradients are computed (in the sense of the material derivative), and the gradient descent method employed to minimize these functionals. Numerical example is given.
In 1970, Pshenichny published a linearization method for nonlinear programming in Russian, which has been overlooked in the English literature. The method is essentially a recursive quadratic programming technique with an active set strategy. Pshenichny has proved global convergence of the method and convergence rate estimates. The method is presented in this paper, with convergence theorems stated. Application of the method is made to shape optimal design, kinematic optimization, and dynamic system optimization. The method is shown to be particularly attractive in utilization of mechanical design sensitivity analysis techniques and performs well on all classes of problems treated.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.