Topic
Discrete optimization
About: Discrete optimization is a research topic. Over the lifetime, 4598 publications have been published within this topic receiving 158297 citations. The topic is also known as: discrete optimisation.
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TL;DR: In this paper, the authors consider the problem of optimizing a high-dimensional convex function using stochastic zeroth-order queries and present two algorithms: a successive component/feature selection algorithm and a noisy mirror descent algorithm using Lasso gradient estimates.
Abstract: We consider the problem of optimizing a high-dimensional convex function using stochastic zeroth-order queries. Under sparsity assumptions on the gradients or function values, we present two algorithms: a successive component/feature selection algorithm and a noisy mirror descent algorithm using Lasso gradient estimates, and show that both algorithms have convergence rates that de- pend only logarithmically on the ambient dimension of the problem. Empirical results confirm our theoretical findings and show that the algorithms we design outperform classical zeroth-order optimization methods in the high-dimensional setting.
33 citations
Proceedings Article•
01 Mar 2007
33 citations
01 May 1999
TL;DR: The sequential quadratic programming (SQP) is applied to solve the robust optimization problem of electromechanical devices considering the uncertainties of design variables based on numerical optimization technique and finite element method.
Abstract: This paper presents the robust shape optimization of electromechanical devices considering the uncertainties of design variables based on numerical optimization technique and finite element method (FEM). In the formulation of robust optimization, the multiobjective function is composed of the mean and the standard deviation of original objective function, while the constraints are supplemented by adding a penalty term to the original constraints. The sequential quadratic programming (SQP) is applied to solve the robust optimization problem. The results of robust shape optimization considering manufacturing errors are compared with those of conventional shape optimization.
33 citations
TL;DR: In this article, an approach to optimize simultaneously the geometry and topology of statically undetermined trusses considering the acting forces and the yielding stress of the bars as random variables is presented.
Abstract: This article deals with the reliability based geometry and topology optimization of truss structures. It presents an approach to optimize simultaneously the geometry and topology of statically undetermined trusses considering the acting forces and the yielding stress of the bars as random variables. Based on the assumptions of linear structural behaviour and independent and normally distributed random variables, the optimization problem is posed in such a way that its computational cost is similar to a standard deterministic optimization problem, which is the main contribution of this study. It is shown in the numerical analysis that when uncertainties are considered, the resulting optimum structure may not be a simply scaled version of the deterministic solution, but there may be a change in the structural geometry as well.
33 citations
TL;DR: In this article, two optimization techniques, namely transformation and controlled enumeration, are employed to solve the optimization problem of truss structures, and results obtained by both methods are compared and appropriate conclusions are drawn.
33 citations