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

By Krister Svanberg. SIAM Journal on Optimization, 2002

827 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9de52ce020703b06709f794d46a3d56c83537908

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Citations in the corpus

Material interpolation schemes for unified topology and multi-material optimization (2011, methodology): “Dual algorithms in combination with convex separable approximations such as the method of moving asymptotes (MMA), see Svanberg (1987, 2002) , have been the natural choice for two-phase topology optimization problems with a large number of variables and few constraints.”
Multi-objective concurrent topology optimization of thermoelastic structures composed of homogeneous porous material (2013, methodology): “In this research, the GCMMA method (Globally Convergent version of the Method of Moving Asymptotes) (Svanberg 2002) is utilized as the optimizer.”
Robust topology optimization under loading uncertainty based on linear elastic theory and orthogonal diagonalization of symmetric matrices (2014, methodology): “(8) Update design variables by MMA optimizer.”
Sequential integer programming methods for stress constrained topology optimization (2007, neutral): “Many optimization methods, such as Sequential linear programming (Griffith and Stewart (1961)), Sequential convex programming (Fleury (1989) and Svanberg (2002) ) and Sequential quadratic programming (see e.g.”
A new multi-objective programming scheme for topology optimization of compliant mechanisms (2009, methodology): “Using concept of convex separable approximations ( Svanberg 2002 ), the MMA scheme transfers the original optimization problem into a sequence of linearized, strictly convex and separable sub-problems.”
Isogeometric design of elastic arches for maximum fundamental frequency (2011, methodology): “The optimisation problem (26) is solved using the globally convergent version of the method of moving asymptotes (GCMMA) (Svanberg 2002).”
Topology optimization of heat conduction problems using the finite volume method (2006, methodology): “The computational procedure used to solve (10) is in this work based on the use of the MMA algorithm; see Svanberg (1987, 2002) .”
Length scale and manufacturability in density-based topology optimization (2016, background): “A number of alternatives have been compared in [118], and the conclusion is that general nonlinear optimization solvers, such as IPOPT [143], often outperformMMA and its globally convergent counterpart GCMMA [133].”
An adaptive multilevel approach to the minimal compliance problem in topology optimization (2005, methodology): “For the sake of space we will omit a detailed description of this method and refer the interested reader to Svanberg [17, 18].”
Topology optimization of a pseudo 3D thermofluid heat sink model (2018, positive): “The optimization is conducted within COMSOL’s Optimization Module which automatically solves the adjoint problem to provide sensitivities for the objective and constraint functionals and the globally convergent version of the Method of Moving Asymp-totes (GCMMA) [44] is used as the optimization meth”