NDLI: A Newton method for solving continuous multiple material minimum compliance problems

Content Provider	Springer Nature Link
Author	Stolpe, Mathias Stegmann, Jan
Copyright Year	2007
Abstract	This paper presents an implementation of an active-set line-search Newton method intended for solving large-scale instances of a class of multiple material minimum compliance problems. The problem is modeled with a convex objective function and linear constraints. At each iteration of the Newton method, one or two linear saddle point systems are solved. These systems involve the Hessian of the objective function, which is both expensive to compute and completely dense. Therefore, the linear algebra is arranged such that the Hessian is not explicitly formed. The main concern is to solve a sequence of closely related problems appearing as the continuous relaxations in a nonlinear branch and bound framework for solving discrete minimum compliance problems. A test-set consisting of eight discrete instances originating from the design of laminated composite structures is presented. Computational experiments with a branch and bound method indicate that the proposed Newton method can, on most instances in the test-set, take advantage of the available starting point information in an enumeration tree and resolve the relaxations after branching with few additional function evaluations. Discrete feasible designs are obtained by a rounding heuristic. Designs with provably good objective functions are presented.
Starting Page	93
Ending Page	106
Page Count	14
File Format	PDF
ISSN	1615147X
Journal	Structural and Multidisciplinary Optimization
Volume Number	35
Issue Number	2
e-ISSN	16151488
Language	English
Publisher	Springer-Verlag
Publisher Date	2007-05-17
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Structural optimization Minimum compliance optimization Newton method Preconditioning Iterative methods Engineering Design Numerical and Computational Methods in Engineering Computer-Aided Engineering (CAD, CAE) and Design Theoretical and Applied Mechanics
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Computer Graphics and Computer-Aided Design Control and Systems Engineering Computer Science Applications Software

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