A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations

Svanberg, Krister

doi:10.1137/s1052623499362822

Cited by 1,058 publications

(650 citation statements)

References 3 publications

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“…Following Svanberg's approach [30], artificial variables w D w 1 ; w 2 ; : : : ; w m T ; w > 0, are introduced into the optimization problem (12), so that the following enlarged problem is addressed. Even if there is an empty solution set for the optimization model (12), a solution with the minimum violating the constraints in Equation (12) can be obtained.…”

Section: A Transferred Approximate Optimization Modelmentioning

confidence: 99%

Continuum structural topological optimizations with stress constraints based on an active constraint technique

Rong

Xiao

et al. 2016

Numerical Meth Engineering

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SUMMARYStress-related problems have not been given the same attention as the minimum compliance topological optimization problem in the literature. Continuum structural topological optimization with stress constraints is of wide engineering application prospect, in which there still are many problems to solve, such as the stress concentration, an equivalent approximate optimization model and etc. A new and effective topological optimization method of continuum structures with the stress constraints and the objective function being the structural volume has been presented in this paper. To solve the stress concentration issue, an approximate stress gradient evaluation for any element is introduced, and a total aggregation normalized stress gradient constraint is constructed for the optimized structure under the r th load case. To obtain stable convergent series solutions and enhance the control on the stress level, two p-norm global stress constraint functions with different indexes are adopted, and some weighting p-norm global stress constraint functions are introduced for any load case. And an equivalent topological optimization model with reduced stress constraints is constructed,being incorporated with the rational approximation for material properties, an active constraint technique, a trust region scheme, and an effective local stress approach like the qp approach to resolve the stress singularity phenomenon. Hence, a set of stress quadratic explicit approximations are constructed, based on stress sensitivities and the method of moving asymptotes. A set of algorithm for the one level optimization problem with artificial variables and many possible non-active design variables is proposed by adopting an inequality constrained nonlinear programming method with simple trust regions, based on the primal-dual theory, in which the non-smooth expressions of the design variable solutions are reformulated as smoothing functions of the Lagrange multipliers by using a novel smoothing function. Finally, a twolevel optimization design scheme with active constraint technique, i.e. varied constraint limits, is proposed to deal with the aggregation constraints that always are of loose constraint (non active constraint) features in the conventional structural optimization method. A novel structural topological optimization method with stress constraints and its algorithm are formed, and examples are provided to demonstrate that the proposed method is feasible and very effective.

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Section: A Transferred Approximate Optimization Modelmentioning

confidence: 99%

Continuum structural topological optimizations with stress constraints based on an active constraint technique

Rong

Xiao

et al. 2016

Numerical Meth Engineering

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“…To guarantee that the sequence of iteration points approaches the solution x * , one may cast the SAO method into a trust region framework (Alexandrov et al 1998), or in a framework of variable conservatism (Svanberg 2002). In the trust region framework, an allowed search domain is defined around x {k} , and incorporated into closed set C .…”

Section: Sequential Approximate Optimizationmentioning

confidence: 99%

“…If the primal subproblems happens to be infeasible, relaxation may for instance be used (see e.g. Svanberg 2002). …”

Section: Sequential Convex Programming Algorithmsmentioning

confidence: 99%

“…Various approaches for enforcing global convergence have also been proposed. These include line search variants of MMA (Zillober 1993), and MMA cast in a framework of variable conservatism (Svanberg 2002). Despite the risk of divergence, the simple 'always accept' strategy is nevertheless frequently adopted and found to be effective and efficient in many a structural optimization application (Groenwold and Etman 2010a).…”

Section: Sequential Convex Programming Algorithmsmentioning

confidence: 99%

“…Well-known examples are the convex linearization (CONLIN) algorithm (Fleury and Braibant 1986) and it's generalization, the method of moving asymptotes (MMA) (Svanberg 1987(Svanberg , 2002. These algorithms-and some related variants, e.g.…”

Section: Introductionmentioning

confidence: 99%

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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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Finite Element Modeling of Viscoelastic Damping by Modal Strain Energy Method

2018

Active and Passive Vibration Damping

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A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations

Cited by 1,058 publications

References 3 publications

Continuum structural topological optimizations with stress constraints based on an active constraint technique

Continuum structural topological optimizations with stress constraints based on an active constraint technique

First-order sequential convex programming using approximate diagonal QP subproblems

Finite Element Modeling of Viscoelastic Damping by Modal Strain Energy Method

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