Showing papers by "Jong-Shi Pang published in 1991"
TL;DR: The algorithm is based on a unified formulation of these three mathematical programming problems as a certain system of B-differentiable equations, and is a modification of the damped Newton method described in Pang (1990) for solving such systems of nonsmooth equations.
Abstract: This paper presents a globally convergent, locally quadratically convergent algorithm for solving general nonlinear programs, nonlinear complementarity and variational inequality problems. The algorithm is based on a unified formulation of these three mathematical programming problems as a certain system of B-differentiable equations, and is a modification of the damped Newton method described in Pang (1990) for solving such systems of nonsmooth equations. The algorithm resembles several existing methods for solving these classes of mathematical programs, but has some special features of its own; in particular, it possesses the combined advantage of fast quadratic rate of convergence of a basic Newton method and the desirable global convergence induced by one-dimensional Armijo line searches. In the context of a nonlinear program, the algorithm is of the sequential quadratic programming type with two distinct characteristics: (i) it makes no use of a penalty function; and (ii) it circumvents the Maratos effect. In the context of the variational inequality/complementarity problem, the algorithm provides a Newton-type descent method that is guaranteed globally convergent without requiring the F-differentiability assumption of the defining B-differentiable equations.
145 citations
TL;DR: This paper presents a globally convergent model algorithm for the minimization of a locally Lipschitzian function, built on an iteration function of two arguments, and the convergence theory is developed parallel to analogous results for the problem of solving systems of locally Lipsonian equations.
Abstract: This paper presents a globally convergent model algorithm for the minimization of a locally Lipschitzian function. The algorithm is built on an iteration function of two arguments, and the convergence theory is developed parallel to analogous results for the problem of solving systems of locally Lipschitzian equations. Application of the theory to a wide range of nonsmooth optimization problems is discussed.These include the minimax problem, the composite optimization problem, the implicit programming problem, and others. A recently developed nonmonotone linesearch technique is shown to be applicable in this nonsmooth context, and an extension to constrained problems is also presented.
53 citations