Complementarity and duality are closely related, multi-disciplinary topics that pervade all natural phenomena, and form the basis for solving many underlying nonconvex or global optimization problems that arise in science and engineering. During the last forty years, much research has been devoted to the development of mathematical modeling, theory, and computational methods in this arena. The field has now matured along many directions, especially in engineering mechanics and design, mathematical physics, economics, optimization, and control.

One common theme in all this is that there is typically some primal problem that is in coNP, and a dual that is in NP, and thus searchable. The dual can give posteriori bounds on the primal, and when there is no duality gap, can provide an exact solution. Duality may also be used to provide proofs verifying the robustness of embedded systems in a network environment, and in creating inference processes for comparing data and models in biological systems. In addition, this provides a unifying framework for treating both vertical, protocol stack decomposition of networks, and horizontal, or distributed and asynchronous control that occur at each level in the stack.

The duality theory of Nonlinear Programming has had profound influence on the theory of Approximation Algorithms for NP-hard optimization problems. Today's application areas, such as Internet problems, network design, and biology, are characterized by massively large problem instances that require reliable solutions, preferably with proven guarantees. The primal-dual schema has been successful in analyzing several such NP-hard problems, providing algorithms with good empirical performance. Recent extensions of this schema to handle non-optimization problems in the nascent area of Algorithmic Game Theory have yielded the first polynomial-time algorithm for computing market equilibria in a framework first introduced by Irving Fischer in 1891 (assuming linear utility functions). Moreover, many new advances in global optimization are enabling the solution of heretofore open, difficult engineering design and process control problems to global optimality for the very first time in the literature.

A primary goal of this CDGO-2005 conference is to bring together engineers, scientists, and mathematicians from a variety of related disciplines, who are at the forefront of their research fields, to exchange ideas and present original high-level unpublished research in the areas of complementarity, duality, and nonconvex or global optimization, with particular interests in the following topics:

• Complementarity in modern mechanics and optimization;
• Duality in variational analysis, economics, and game theory;
• Primal-dual methods and algorithms in computational sciences;
• Min-max theory in mathematical analysis and discrete optimization;
• Global optimization theory and algorithms;
• Applications in internet problems, network design, and biology;
• Natural duality and unity in philosophy, system science, cybernetics, and informatics.