Krannert Graduate School of Management
4026, Rawls Hall
phone: (765) 496-2620
My resume (html,ps,pdf)
My Dissertation Abstract
My e-optimization page
Research Interests (publications)
Classical nonlinear programming algorithms have primarily concerned themselves with local optimization ensuring globality only under the restrictive assumptions of convexity. My research is focussed on finding ways to relax this requirement without sacrificing too much in terms of efficiency. It may sound ironical, but the most powerful tool in our hands turns out to be convex analysis. Using convexification techniques, we develop new algorithmic strategies for zeroing in on the global optima of continuous, integer and mixed integer nonlinear programming problems.
The techniques developed as a result of this research are incorporated in our global optimization package, BARON (Branch and Reduce Optimization Navigator), on a continual basis, which then serves as a test-bed for the proposed schemes. BARON is a MINLP solver that incorporates advanced domain reduction schemes with automatic reformulation strategies in order to locate the global optimum for the given problem. In its short existence on the web, we have had 120 researchers submit over 5500 problems to it. 7 PhD students are using our solver to solve application problems.
Problems proposed in various scientific and engineering disciplines can be posed as mixed integer nonlinear programs. To name a few such applications: molecular design, parameter estimation, fixture design, process synthesis, heat exchanger network design, pooling problems, power economies of scale, just-in-time manufacturing. The list can go on and on ... However, the lack of viable solution methodologies has hampered the research using this line of approach. This situation is changing rapidly. A considerable amount of success has been achieved and problems heretofore considered intractable can now be solved with a modest computational effort. I am interested in exploring such application areas, where ideas from global optimization literature can help immensely.
Certain classes of global optimization problems are amenable to specialized treatment as a result of their unique problem structure. I am interested in identifying such classes and in developing new efficient algorithms for their solution. Stochastic integer programming, factorable nonlinear programming, separable concave programming, multiplicative programming and fractional programming are some of the areas in which we have been able to contribute specialized algorithms.