The following tutorials are planned for the International Conference on Complementarity, Duality, and Global Optimization in Science and Engineering Conference

Hoang Tuy, Ph.D.

Institute of Mathematics
National Center for Science and Technology
Hanoi, Vietnam

Title: Monotonic Optimization: Theory and Application

Abstract: A function f : Rn _ R is said to be increasing if f(x') >= f(x) whenever x' >= x (component wise); decreasing if _f(x) is increasing; a d.m. function if it is the difference of two increasing functions. In recent years a theory of monotonic optimization has been developed to provide a mathematical framework for studying optimization problems.

In this tutorial we will present the basic concepts, tools, methods and applications of monotonic optimization, with particular emphasis on separation and monotonicity cuts, underlying polyblock approximation and branch and cut methods for solving continuous and discrete optimization problems. Robust methods of nonconvex optimization will also be discussed, as well as applications to some hard problems of global optimization such as generalized polynomial programming, generalized multiplicative and fractional programming, optimization over the efficient set, bi-level programming and complementarity problems.

Michael C. Ferris, Ph.D.

University of Wisconsin
Department of Computer Sciences

Title: Complementarity Problems and Applications

Abstract: While optimizers are familiar with complementary slackness as the optimality conditions of linear and nonlinear programming, complementarity problems arise naturally in many practical applications from engineering and economics. Examples include applied general equilibrium modeling, traffic network design, structural engineering and finance. Several examples will be outlined, together with an overview of modeling and solution techniques.

Recent interest in optimization problems with complementarity constraints, or the more general class of MPEC's has rekindled the interest in nonlinear programming approaches to treat complementarity conditions. We outline basic ideas, highlight several computational schemes and explain their utility by application. A brief description of the extended modeling paradigm of EPEC's will be given.

Janos D. Pinter, PhD, DSc

President & Research Scientist, PCS Inc., Halifax, NS, Canada
Adjunct Professor, Dalhousie University, Halifax, NS, Canada
Research Fellow, University of Ballarat, Vic., Australia

Title: Global Optimization - Software Development and Advanced Applications

Abstract: The objective of global optimization (GO) is to find the 'absolutely best' solution in nonlinear decision models that may also have a multitude of local optima. Finding such solutions (numerically) requires global scope search algorithms.

We have been developing GO algorithms and software implementations for over a decade. The currently available implementation platforms include compilers (C, Fortran), Excel, modeling languages (AIMMS, GAMS, MPL), and the integrated computing systems Maple, Mathematica, and MATLAB (via TOMLAB).

A concise summary of these developments is presented, including algorithm background, software, GO test examples and challenges, and a review of existing and prospective applications in the sciences, engineering, and economics.