Interior-Point Methods for Nonlinear Optimization and Complementarity

Princeton University, Princeton NJ

Investigators

Abstract

Proposal #0098040 Princeton University Vanderbei, Robert J. Optimization is the process of determining values of certain controllable parameters so as to achieve the best, i.e. smallest or largest, value of an objective function within a specified domain of feasible parameter settings. The demand for high-performance optimization algorithms and software is increasing rapidly as the power of the current technology to solve difficult real-world problems is becoming more widely recognized. Much of the success of modern optimization techiques stems from the recent development of so-called interior-point methods. These methods were first developed for linear optimization problems but are now actively being extended to nonlinear optimization problems. This research involves the development of new interior-point algorithms and software for large-scale nonlinear constrained optimization. Specific goals include: (1) fundamental enhancements to the current state-of-the-art, such as the replacement of the merit-function for step-length control with a filter-based method and the development of better techniques to detect unbounded and infeasible problems; (2) extension of the basic algorithm to new problem classes, such as second-order cone programming and semidefinite programming, that don't quite fit the basic paradigm of nonlinear constrained optimization; (3) further extension beyond the realm of optimization to nonlinear complementarity problems, which arise in many engineering problems; and finally (4) development of a large repository of optimization models, which serves both to illustrate the power of modern optimization technology and also to provide a test bed for future algorithm development.