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Author: Stanford University. Engineering-Economic Systems and Operations Research Department. Systems Optimization Laboratory Publisher: ISBN: Category : Linear programming Languages : en Pages : 18
Book Description
Abstract: "We discuss methods for solving the key linear equations (KKT systems) within primal-dual barrier methods for linear programming. To allow sparse indefinite Cholesky-type factorizations of the KKT systems, we perturb the problem slightly. Perturbations improve the stability of the Cholesky factorizations, but affect the efficiency of the cross-over to simplex (to obtain a basic solution to the original problem). We explore these effects by running OSL on the larger Netlib examples."
Author: Stanford University. Engineering-Economic Systems and Operations Research Department. Systems Optimization Laboratory Publisher: ISBN: Category : Linear programming Languages : en Pages : 18
Book Description
Abstract: "We discuss methods for solving the key linear equations (KKT systems) within primal-dual barrier methods for linear programming. To allow sparse indefinite Cholesky-type factorizations of the KKT systems, we perturb the problem slightly. Perturbations improve the stability of the Cholesky factorizations, but affect the efficiency of the cross-over to simplex (to obtain a basic solution to the original problem). We explore these effects by running OSL on the larger Netlib examples."
Author: Stanford University. Engineering-Economic Systems and Operations Research Department. Systems Optimization Laboratory Publisher: ISBN: Category : Linear programming Languages : en Pages : 16
Book Description
Abstract: "We discuss methods for solving the key linear equations within primal-dual barrier methods for linear and quadratic programming. Following Freund and Jarre, we explore methods for reducing the Newton equations to 2 X 2 block systems (KKT systems) in a stable manner. Some methods require partitioning the variables into two or more parts, but a simpler approach is derived and recommended. To justify symmetrizing the KKT systems, we assume the use of a sparse solver whose numerical properties are independent of row and column scaling. In particular, we regularize the problem and use indefinite Cholesky-type factorizations. An implementation within OSL is tested on the larger NETLIB examples."
Author: Géry de Saxcé Publisher: Springer Science & Business Media ISBN: 9400754256 Category : Science Languages : en Pages : 220
Book Description
To determine the carrying capacity of a structure or a structural element susceptible to operate beyond the elastic limit is an important task in many situations of both mechanical and civil engineering. The so-called “direct methods” play an increasing role due to the fact that they allow rapid access to the request information in mathematically constructive manners. They embrace Limit Analysis, the most developed approach now widely used, and Shakedown Analysis, a powerful extension to the variable repeated loads potentially more economical than step-by-step inelastic analysis. This book is the outcome of a workshop held at the University of Sciences and Technology of Lille. The individual contributions stem from the areas of new numerical developments rendering this methods more attractive for industrial design, extension of the general methodology to new horizons, probabilistic approaches and concrete technological applications.
Author: Aeneas Marxen Publisher: ISBN: Category : Linear programming Languages : en Pages : 86
Book Description
Abstract: "The linear program min c[superscript T]x subject to Ax=b, x [greater than or equal to] 0, is solved by the projected Newton barrier method. The method consists of solving a sequence of subproblems of the form [formula] subject to Ax=b. Extensions for upper bounds, free and fixed variables are given. A linear modification is made to the logarithmic barrier function, which results in the solution being bounded in all cases. It also facilitates the provision of a good starting point. The solution of each subproblem involves repeatedly computing a search direction and taking a step along this direction. Ways to find an initial feasible solution, step sizes and convergence criteria are discussed.
Author: Stanford University. Engineering-Economic Systems and Operations Research Department. Systems Optimization Laboratory
Author: Stanford University. Engineering-Economic Systems and Operations Research Department. Systems Optimization Laboratory
Author: M. A. Saunders
Author: Stanford University. Department of Operations Research. Systems Optimization Laboratory
Author: Stanford University. Engineering-Economic Systems and Operations Research Department. Systems Optimization Laboratory
Author: 
Author: Loyce M. Adams
Author: Géry de Saxcé
Author: Stanford University. Department of Operations Research. Systems Optimization Laboratory
Author: Aeneas Marxen
Author: Stanford University. Department of Operations Research. Systems Optimization Laboratory