Very large scale optimization by sequential convex programming

Zillober, Christian; Schittkowski, Klaus; Moritzen, K.

doi:10.1080/10556780410001647195

Cited by 25 publications

(9 citation statements)

References 19 publications

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“…see Fleury (1993), Zillober et al (2004), and Duysinx et al (2009). Examples of established algorithms within this class include CONLIN by Fleury and Braibant (1986) and the method of moving asymptotes (MMA) by Svanberg (1987).…”

Section: Introductionmentioning

confidence: 99%

“…Examples of established algorithms within this class include CONLIN by Fleury and Braibant (1986) and the method of moving asymptotes (MMA) by Svanberg (1987). Algorithmic variants of MMA were presented by, for example, Borrvall and Petersson (2001), Bruyneel et al (2002), and Zillober et al (2004). Groenwold and Etman (2008b) presented tailorable convex separable SAO algorithms, in which convexity and separability of the approximations was used for the efficient solution of the approximate optimization subproblems.…”

Section: Introductionmentioning

confidence: 99%

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On the conditional acceptance of iterates in SAO algorithms based on convex separable approximations

Groenwold

Etman

2010

Struct Multidisc Optim

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We reflect on the convergence and termination of optimization algorithms based on convex and separable approximations using two recently proposed strategies, namely a trust region with filtered acceptance of the iterates, and conservatism. We then propose a new strategy for convergence and termination, denoted f iltered conservatism, in which the acceptance or rejection of an iterate is determined using the nonlinear acceptance filter. However, if an iterate is rejected, we increase the conservatism of every unconservative approximation, rather than reducing the trust region. Filtered conservatism aims to combine the salient features of trust region strategies with nonlinear acceptance filters on the one hand, and conservatism on the other. In filtered conservatism, the nonlinear acceptance filter is used to decide if an iterate is accepted or rejected. This allows for the acceptance of infeasible iterates, which would not be accepted in a method based on conservatism. If however an iterate is rejected, the trust region need not be decreased; it may be kept constant. Convergence is than effected by increasing the conservatism of only the unconservative approximations in the (large, constant) trust region, until the iterate becomes acceptable to the filter. Numerical results corroborate the accuracy and robustness of the method.Based on the paper entitled 'Globally convergent SAO algorithms for large scale simulation-based optimization', presented at the 8th World

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the conditional acceptance of iterates in SAO algorithms based on convex separable approximations

Groenwold

Etman

2010

Struct Multidisc Optim

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“…These algorithms-and some related variants, e.g. see Borrval and Petersson (2001), Bruyneel et al (2002) and Zillober et al (2004)-are also known as sequential convex programming (SCP) methods (Fleury 1993;Zillober et al 2004;Duysinx et al 2009). …”

Section: Introductionmentioning

confidence: 99%

“…In many of the cited references, the dual formulation of Falk is used (Falk 1967;Fleury 1979), but other efficient subproblem solvers have also been proposed, see e.g. Zillober (2001) and Zillober et al (2004).…”

Section: Introductionmentioning

confidence: 99%

First-order sequential convex programming using approximate diagonal QP subproblems

Etman

Groenwold

Rooda

2011

Struct Multidisc Optim

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Optimization algorithms based on convex separable approximations for optimal structural design often use reciprocal-like approximations in a dual setting; CONLIN and the method of moving asymptotes (MMA) are wellknown examples of such sequential convex programming (SCP) algorithms. We have previously demonstrated that replacement of these nonlinear (reciprocal) approximations by their own second order Taylor series expansion provides a powerful new algorithmic option within the SCP class of algorithms. This note shows that the quadratic treatment of the original nonlinear approximations also enables the restatement of the SCP as a series of Lagrange-Newton QP subproblems. This results in a diagonal trust-region SQP type of algorithm, in which the second order diagonal terms are estimated from the nonlinear (reciprocal) intervening variables, rather than from historic information using an exact or a quasi-Newton Hessian approach. The QP formulation seems particularly attractive for problems with far more constraints than variables (when pure dual methods are at a disadvantage), or when both the number of design variables and the number of (active) constraints is very large.

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“…Large scale problems can be handled by different variants of the solution procedure for the subproblem, see Zillober et al [53], where sparsity of problem data can be exploited.…”

Section: Sequential Convex Programmingmentioning

confidence: 99%

Nonlinear Programming: Algorithms, Software, and Applications

Schittkowski

Zillober

2005

IFIP International Federation for Information Processing

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A b s t r a c tWe introduce some methods for constrained nonlinear programming that are widely used in practice and that are known under the names SQP for sequential quadratic programming and SCP for sequential convex programming. In both cases, convex subproblems are formulated, in the first case a quadratic programming problem, in the second case a separable nonlinear program in inverse variables. The methods are outlined in a uniform way and the results of some comparative performance tests are listed. We especially show the suitability of sequential convex programming methods to solve some classes of very large scale nonlinear programs, where implicitly defined systems of equations seem to support the usage of inverse approximations. The areas of interest are structural mechanical optimization, i.e., topology optimization, and optimal control of partial differential equations after a full discretization. In addition, a few industrial applications and case studies are shown to illustrate practical situations under which the codes implemented by the authors are in use.

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Very large scale optimization by sequential convex programming

Cited by 25 publications

References 19 publications

On the conditional acceptance of iterates in SAO algorithms based on convex separable approximations

On the conditional acceptance of iterates in SAO algorithms based on convex separable approximations

First-order sequential convex programming using approximate diagonal QP subproblems

Nonlinear Programming: Algorithms, Software, and Applications

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