On convergence of a global search strategy for reverse convex problems.
Strekalovsky, Alexander (2005)
Journal of Applied Mathematics and Decision Sciences
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Strekalovsky, Alexander (2005)
Journal of Applied Mathematics and Decision Sciences
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Marek Libura (2009)
Control and Cybernetics
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Ali, M.S.S. (2005)
International Journal of Mathematics and Mathematical Sciences
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Samuel Amstutz (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper deals with topology optimization of domains subject to a pointwise constraint on the gradient of the state. To realize this constraint, a class of penalty functionals is introduced and the expression of the corresponding topological derivative is obtained for the Laplace equation in two space dimensions. An algorithm based on these concepts is proposed. It is illustrated by some numerical applications.
Dominique Azé, Jean-Noël Corvellec (2004)
ESAIM: Control, Optimisation and Calculus of Variations
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Refining the variational method introduced in Azé et al. [Nonlinear Anal. 49 (2002) 643-670], we give characterizations of the existence of so-called global and local error bounds, for lower semicontinuous functions defined on complete metric spaces. We thus provide a systematic and synthetic approach to the subject, emphasizing the special case of convex functions defined on arbitrary Banach spaces (refining the abstract part of Azé and Corvellec [SIAM J. Optim. 12 (2002) 913-927],...
Arkadii Kryazhimskii (2001)
International Journal of Applied Mathematics and Computer Science
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For a class of infinite-dimensional minimization problems with nonlinear equality constraints, an iterative algorithm for finding global solutions is suggested. A key assumption is the convexity of the ''epigraph'', a set in the product of the image spaces of the constraint and objective functions. A convexification method involving randomization is used. The algorithm is based on the extremal shift control principle due to N.N. Krasovskii. An application to a problem of optimal control...