Methods for Large-scale Extended Linear-quadratic Programming PDF Download

Author: Ciyou Zhu
Publisher:
ISBN:
Category : Quadratic programming
Languages : en
Pages : 180

View

Book Description

Author: Gianni Pillo
Publisher: Springer Science & Business Media
ISBN: 0387300651
Category : Mathematics
Languages : en
Pages : 297

View

Book Description
This book reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research. Individual chapters, contributed by eminent authorities, provide an up-to-date overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications.

Author: Yves Dominique Brise
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832533664
Category : Computers
Languages : en
Pages : 232

View

Book Description
This PhD thesis was written at ETH Zurich, in Prof. Dr. Emo Welzl's research group, under the supervision of Dr. Bernd Garnter. It shows two theoretical results that are both related to quadratic programming. The first one concerns the abstract optimization framework of violator spaces and the randomized procedure called Clarkson's algorithm. In a nutshell, the algorithm randomly samples from a set of constraints, computes an optimal solution subject to these constraints, and then checks whether the ignored constraints violate the solution. If not, some form of re-sampling occurs. We present the algorithm in the easiest version that can still be analyzed successfully. The second contribution concerns quadratic programming more directly. It is well-known that a simplex-like procedure can be applied to quadratic programming. The main computational effort in this algorithm comes from solving a series of linear equation systems that change gradually. We develop the integral LU decomposition of matrices, which allows us to solve the equation systems efficiently and to exploit sparse inputs. Last but not least, a considerable portion of the work included in this thesis was devoted to implementing the integral LU decomposition in the framework of the existing quadratic programming solver in the Computational Geometry Algorithms Library (CGAL). In the last two chapters we describe our implementation and the experimental results we obtained.

Author: Susana Gomez
Publisher: SIAM
ISBN: 9780898712698
Category : Mathematics
Languages : en
Pages : 388

View

Book Description
The papers in this volume emphasize the numerical aspects of three main areas: optimization, linear algebra and partial differential equations. Held in January, 1989, in Yucatan, Mexico, the workshop was organized by the Institute for Research in Applied Mathematics of the National University of Mexico in collaboration with the mathematical Sciences Department at Rice University.

Author:
Publisher: DIANE Publishing
ISBN: 1428995633
Category :
Languages : en
Pages : 55

View

Book Description

Author: Ding-Zhu Du
Publisher: Springer Science & Business Media
ISBN: 1461335574
Category : Computers
Languages : en
Pages : 300

View

Book Description
Techniques and principles of minimax theory play a key role in many areas of research, including game theory, optimization, and computational complexity. In general, a minimax problem can be formulated as min max f(x, y) (1) ",EX !lEY where f(x, y) is a function defined on the product of X and Y spaces. There are two basic issues regarding minimax problems: The first issue concerns the establishment of sufficient and necessary conditions for equality minmaxf(x,y) = maxminf(x,y). (2) "'EX !lEY !lEY "'EX The classical minimax theorem of von Neumann is a result of this type. Duality theory in linear and convex quadratic programming interprets minimax theory in a different way. The second issue concerns the establishment of sufficient and necessary conditions for values of the variables x and y that achieve the global minimax function value f(x*, y*) = minmaxf(x, y). (3) "'EX !lEY There are two developments in minimax theory that we would like to mention.

Author: Stanford University. Department of Operations Research. Systems Optimization Laboratory
Publisher:
ISBN:
Category :
Languages : en
Pages : 142

View

Book Description

Author: Wenyu Sun
Publisher: Springer Science & Business Media
ISBN: 0387249761
Category : Mathematics
Languages : en
Pages : 689

View

Book Description
Optimization Theory and Methods can be used as a textbook for an optimization course for graduates and senior undergraduates. It is the result of the author's teaching and research over the past decade. It describes optimization theory and several powerful methods. For most methods, the book discusses an idea’s motivation, studies the derivation, establishes the global and local convergence, describes algorithmic steps, and discusses the numerical performance.

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 14

View

Book Description
Research under this grant has focused on large-scale optimization methodology connected with the solution of problems in which decisions must be made in the face of uncertainty: stochastic programming problems. The principal techniques developed for modeling such problems have been used, including various new kinds of decomposition into small-scale optimization problems in extended linear-quadratic programming. Extended linear-quadratic programming goes beyond ordinary linear and quadratic programming in allowing for objective functions to incorporate penalty terms and other features that create piecewise linear or quadratic formulas. The new decomposition techniques include primal-dual Lagrangian decomposition and forward-backward splitting. In total, the 4-year grant supported the writing of 16 technical papers (12 already in print or about to be), the development and documentation of 2 computer codes, and the completion of 3 doctoral dissertations.

Author: Karl Frauendorfer
Publisher: Springer Science & Business Media
ISBN: 3642956963
Category : Business & Economics
Languages : en
Pages : 236

View

Book Description
Stochastic Programming offers models and methods for decision problems wheresome of the data are uncertain. These models have features and structural properties which are preferably exploited by SP methods within the solution process. This work contributes to the methodology for two-stagemodels. In these models the objective function is given as an integral, whose integrand depends on a random vector, on its probability measure and on a decision. The main results of this work have been derived with the intention to ease these difficulties: After investigating duality relations for convex optimization problems with supply/demand and prices being treated as parameters, a stability criterion is stated and proves subdifferentiability of the value function. This criterion is employed for proving the existence of bilinear functions, which minorize/majorize the integrand. Additionally, these minorants/majorants support the integrand on generalized barycenters of simplicial faces of specially shaped polytopes and amount to an approach which is denoted barycentric approximation scheme.