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An active set algorithm for tracing parametrized optimaOptimization problems often depend on parameters that define constraints or objective functions. It is often necessary to know the effect of a change in a parameter on the optimum solution. An algorithm is presented here for tracking paths of optimal solutions of inequality constrained nonlinear programming problems as a function of a parameter. The proposed algorithm employs homotopy zero-curve tracing techniques to track segments where the set of active constraints is unchanged. The transition between segments is handled by considering all possible sets of active constraints and eliminating nonoptimal ones based on the signs of the Lagrange multipliers and the derivatives of the optimal solutions with respect to the parameter. A spring-mass problem is used to illustrate all possible kinds of transition events, and the algorithm is applied to a well-known ten-bar truss structural optimization problem.
Document ID
19910046606
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Rakowska, J.
(Virginia Polytechnic Inst. and State Univ. Blacksburg, VA, United States)
Haftka, R. T.
(Virginia Polytechnic Inst. and State Univ. Blacksburg, VA, United States)
Watson, L. T.
(Virginia Polytechnic Institute and State University Blacksburg, United States)
Date Acquired
August 14, 2013
Publication Date
March 1, 1991
Publication Information
Publication: Structural Optimization
Volume: 3
ISSN: 0934-4373
Subject Category
Structural Mechanics
Accession Number
91A31229
Funding Number(s)
CONTRACT_GRANT: DE-FG05-88ER-25068
CONTRACT_GRANT: NAG1-224
CONTRACT_GRANT: AF-AFOSR-89-0497
Distribution Limits
Public
Copyright
Other

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