Ding-Zhu Du, University of Texas, Arlington, USA, dzdu@utdallas.edu Title: Optimization Problems in Under Water Sensor Networks Abstract:Under water sensor network is an important research direction in computer science. There are many interesting optimization problems regarding its design, rounting and applications. In this talk, I'm going to introduce some new research works done by our research group at University of Texas at Dallas, including Donghyun Kim, James Willson, Nassim Sohaee and Weili Wu.
Shu-Cherng Fang, North Carolina State University,fang@ncsu.edu Title: Optimization with Max-Min Fuzzy Relational Equations Abstract: Fuzzy relational equation is the key to fuzzy control. Finding a solution to a system of fuzzy relational equations is mathematically difficult because the involving algebraic operators may have no inverse operation. Finding an optimal solution of an objective function subject to a system of fuzzy relational equations is a challenging global optimization problem due to its special combinatorial nature. In his talk, we give an overview of this class of problems and report some recent progress.
C. Floudas ,Princeton University, floudas@titan.princeton.edu Title: Recent Advances and Challenges in Deterministic Global Optimization Abstract:In this presentation, we will provide an overview of the research progress in global optimization. The focus will be on important contributions during the last five years, and will provide a perspective for future research opportunities. The overview will cover the areas of (a) twice continuously differentiable constrained nonlinear optimization, and (b) mixed-integer nonlinear optimization models. Subsequently, we will present our recent fundamental advances in (i) convex envelope results for multi-linear functions, (ii) a piecewise quadratic convex underestimator for twice continuously differentiable functions, (iii) the generalized alpha-BB framework, (iv) our recently improved convex underestimation techniques for univariate and multivariate functions, and (v) generalized pooling problems. Computational studies will illustrate the potential of these advances.
David Y. Gao, Department of Mathematics,Virginia Tech,Blacksburg, VA 24061, USA, gao@vt.edu Title: Canonical Duality Theory: Unified Understanding of Global Optimization Abstract: Duality is a beautiful, inspiring, and fundamental concept that underlies all natural phenomena. In mathematical economics, dynamical systems, global optimization, control theory, management and decision science, numerical methods and scientific computation, duality principles and methods are playing more and more important roles. The canonical duality theory is a newly developed, potentially powerful methodology, which can be used to model complex systems with a unified solution to a wide class of discrete and continuous problems in global optimization and nonconvex analysis. In this lecture, the speaker will present a brief introduction to the canonical duality theory and its role in global optimization. He will show that many well-known methods and theories, including the variational inequality and complementarity theory, semi-definite and semi-infinite programming methods, etc, can be put in a unified framework. The traditional Lagrangian multiplier method and modern duality theory will be explained in a unified way. He will show that by using the canonical duality theory, a unified analytical solution can be obtained for a large class of problems in global optimization, and both global and local optimality conditions can be identified by a triality theory. Applications will be illustrated by certain well-known global optimization problems, including general polynomial minimization, fractional programming, mixed integer optimization, sensor network localization, and general nonconvex minimization with nonconvex constraints. This talk should bring some fundamentally new insights into global optimization and complex systems theory.
Panos M. Pardalos, University of Florida, pardalos@cao.ise.ufl.edu Title:
Yin-Yu Ye, Stanford University, yinyu-ye@stanford.edu Title:A Unified Theorem on Semidefinite Programming Rank Reduction and its Applications Abstract:We present a unified theorem on semidefinite programming solution rank reduction that provides a unified treatment of and generalizes several well--known results in the literature. In particular, it contains as special cases the Johnson--Lindenstrauss lemma on dimensionality reduction, results on low--distortion embedding into low--dimensional Euclidean space, and approximation results on certain quadratic optimization problems. We also illustrate its applications on semidefinite programming (SDP) based model and method for the position estimation problem in Euclidean distance geometry such as graph realization and wireless sensor network localization. We develop an SDP relaxation model and use the duality theory to derive necessary and/or sufficient conditions for whether a network is "localizable" or not, when the distance measures are accurate.