Optimization problems arise in engineering, business, and medicine. Computational studies show that interior-point methods outperform others for solving large-scale problems. This research involves the development of techniques to improve interior-point methods for nonlinear and related optimization problems. Its intellectual merit is the solution of complex problems and their re-solution under changing conditions, two current deficiencies that must be addressed to keep these methods at the forefront of optimization technology. Test problems benefit the optimization community and researchers in applied fields by encouraging the use of appropriate modeling and solution techniques and the development of new ones as necessary. The broadest impact of this research is the social and financial gains achieved by solving problems that better reflect the real-world and by responding more effectively to a dynamic environment.
In order to improve and extend the use of interior-point methods, the investigators study (1) primal-dual penalty methods to improve warm-starting capabilities for solving closely related problems with changing data and problem size, (2) bilevel frameworks for solving mixed-integer nonlinear problems, with improved warm-starting and infeasibility identification schemes for nonlinear subproblems, and (3) incorporation of equilibrium and cone constraints into the nonlinear optimization framework using the primal-dual penalty approach. Another component of this research is the development and dissemination of a repository of applied problems with a variety of components, such as nonlinear functions, discrete variables, equilibrium constraints, and cone constraints, along with alternate data sets and parameter settings suitable for testing warm-start approaches. All work is incorporated into graduate courses and research. Course notes and test models are distributed on the WWW, and software is made available for free use on the NEOS Server.
