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Solving nonconvex optimization problems
IEEE Control Systems, 2004It is well known that most analysis and design problems in robust and nonlinear control can be formulated as global optimization problems with polynomial objective functions and constraints. The objective of this article is to show how GloptiPoly can solve challenging nonconvex optimization problems in robust nonlinear control.
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Manifold Sampling for $\ell_1$ Nonconvex Optimization
SIAM Journal on Optimization, 2016Summary: We present a new algorithm, called manifold sampling, for the unconstrained minimization of a nonsmooth composite function \(h\circ F\) when \(h\) has known structure. In particular, by classifying points in the domain of the nonsmooth function \(h\) into manifolds, we adapt search directions within a trust-region framework based on knowledge ...
Larson, Jeffrey +2 more
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Nonconvex Semi-infinite Optimization
2018In this chapter we continue the study of SIPs in infinite-dimensional spaces while considering now problems without any convexity assumptions.
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Nonconvex Structural Optimization Problems
Journal of the Engineering Mechanics Division, 1973Plastic optimization problems involving convex specific cost functions can be handled by several methods. The earliest technique was based on the uniform energy dissipation principle; a more general approach which could be termed the cost gradiend method was developed later and was extended to multiload, multicomponent systems and to preassigned ...
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