Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Abstract In this Lecture, dual methods for solving constrained optimization problems are presented. These methods proceed by maximizing a dual function which depends only on the Lagrangian multipliers associated with the constraints. The Lagrangian multipliers, also called dual variables, are required to remain non-negative. The dual method approach is specially useful and efficient when dealing with convex, separable problems. In order to apply dual methods to general problems, a successful strategy consists of using convex approximation schemes. In this “Sequential Convex Programming” (SCP) approach, the primary optimization problem is replaced with a sequence of convex explicit subproblems having a simple algebraic form. Various SCP techniques have recently emerged, that have demonstrated strong potential for efficient solution of structural optimization problems. To illustrate the SCP approach, emphasis will be placed on the “Convex Linearization” (CONLIN) method, because it leads to a relatively simple dual formulation. Next, attention is focused on convex, separable, quadratic problems for which the dual function can be written explicitly as a quadratic (but not separable) form. Efficient second order algorithms based on update formulas for the inverse Hessian matrix are presented. It is finally shown how general separable problems can be solved as a sequence of quadratic subproblems.
Abstract In this Lecture, dual methods for solving constrained optimization problems are presented. These methods proceed by maximizing a dual function which depends only on the Lagrangian multipliers associated with the constraints. The Lagrangian multipliers, also called dual variables, are required to remain non-negative. The dual method approach is specially useful and efficient when dealing with convex, separable problems. In order to apply dual methods to general problems, a successful strategy consists of using convex approximation schemes. In this “Sequential Convex Programming” (SCP) approach, the primary optimization problem is replaced with a sequence of convex explicit subproblems having a simple algebraic form. Various SCP techniques have recently emerged, that have demonstrated strong potential for efficient solution of structural optimization problems. To illustrate the SCP approach, emphasis will be placed on the “Convex Linearization” (CONLIN) method, because it leads to a relatively simple dual formulation. Next, attention is focused on convex, separable, quadratic problems for which the dual function can be written explicitly as a quadratic (but not separable) form. Efficient second order algorithms based on update formulas for the inverse Hessian matrix are presented. It is finally shown how general separable problems can be solved as a sequence of quadratic subproblems.
Dual Methods for Convex Separable Problems
Fleury, C. (Autor:in)
01.01.1993
22 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
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