(577c) Mips Vs Mpccs: A Perspective for Process Engineering

Process optimization problems are characterized by discrete and continuous variables. Breakthrough research by Grossmann and co-workers has pioneered the development and application of mixed integer programming (MIP) for a broad spectrum of optimization tasks in design, operations and control. In many cases, a complementary approach can also be considered through the formulation and solution of mathematical programs with complementarity constraints (MPCCs). Unlike MIPs, MPCCs are formulated as nonlinear programs with nonsmooth elements, which require special attention in the solution process, and locally optimal solutions of these problems can be determined through the direct solution of stationarity conditions. Often, MPCC solutions can be obtained efficiently with large-scale NLP solvers, which makes MPCC formulations desirable in certain settings.

This talk presents a brief perspective of recently developed MPCC solution strategies and applications with emphasis on:

- presentation of stationarity conditions that are used to characterize optimal MPCC solutions.

- pros and cons of NLP-based solution strategies for MPCCs

- process applications in process design, scheduling of nonlinear processes and dynamic optimization

- qualitative comparisons of MIP vs. MPCC strategies

Concluding remarks will address the future potential of MIP, MPCC or hybrid formulations, for particular process applications.