Solution Of P Matrix Linear Complementarity Problems Using A Potential Reduction Algorithm
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Solution of P-matrix Linear Complementarity Problems Using a Potential Reduction Algorithm
Abstract: "We extend our convergence result [25] of a potential reduction algorithm for the P-matrix linear complementarity problem (LCP) to the P0-matrix LCP. We present computational experience with PSD- matrix, P-matrix and P0-matrix LCPs to reinforce our theoretical development. These test problems include random (positive semi-definite) test problems, the worst case examples of Murty and Fathi, and various LCPs arising in engineering problems. We also illustrate how row and column scaling may improve the practical efficiency of the algorithm."
A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems
Author: Hanif D. Sherali
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-04-17
This book deals with the theory and applications of the Reformulation- Linearization/Convexification Technique (RL T) for solving nonconvex optimization problems. A unified treatment of discrete and continuous nonconvex programming problems is presented using this approach. In essence, the bridge between these two types of nonconvexities is made via a polynomial representation of discrete constraints. For example, the binariness on a 0-1 variable x . can be equivalently J expressed as the polynomial constraint x . (1-x . ) = 0. The motivation for this book is J J the role of tight linear/convex programming representations or relaxations in solving such discrete and continuous nonconvex programming problems. The principal thrust is to commence with a model that affords a useful representation and structure, and then to further strengthen this representation through automatic reformulation and constraint generation techniques. As mentioned above, the focal point of this book is the development and application of RL T for use as an automatic reformulation procedure, and also, to generate strong valid inequalities. The RLT operates in two phases. In the Reformulation Phase, certain types of additional implied polynomial constraints, that include the aforementioned constraints in the case of binary variables, are appended to the problem. The resulting problem is subsequently linearized, except that certain convex constraints are sometimes retained in XV particular special cases, in the Linearization/Convexijication Phase. This is done via the definition of suitable new variables to replace each distinct variable-product term. The higher dimensional representation yields a linear (or convex) programming relaxation.
Advances in Optimization and Numerical Analysis
Author: S. Gomez
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-09
In January 1992, the Sixth Workshop on Optimization and Numerical Analysis was held in the heart of the Mixteco-Zapoteca region, in the city of Oaxaca, Mexico, a beautiful and culturally rich site in ancient, colonial and modern Mexican civiliza tion. The Workshop was organized by the Numerical Analysis Department at the Institute of Research in Applied Mathematics of the National University of Mexico in collaboration with the Mathematical Sciences Department at Rice University, as were the previous ones in 1978, 1979, 1981, 1984 and 1989. As were the third, fourth, and fifth workshops, this one was supported by a grant from the Mexican National Council for Science and Technology, and the US National Science Foundation, as part of the joint Scientific and Technical Cooperation Program existing between these two countries. The participation of many of the leading figures in the field resulted in a good representation of the state of the art in Continuous Optimization, and in an over view of several topics including Numerical Methods for Diffusion-Advection PDE problems as well as some Numerical Linear Algebraic Methods to solve related pro blems. This book collects some of the papers given at this Workshop.