11,178 research outputs found
Dual methods and approximation concepts in structural synthesis
Approximation concepts and dual method algorithms are combined to create a method for minimum weight design of structural systems. Approximation concepts convert the basic mathematical programming statement of the structural synthesis problem into a sequence of explicit primal problems of separable form. These problems are solved by constructing explicit dual functions, which are maximized subject to nonnegativity constraints on the dual variables. It is shown that the joining together of approximation concepts and dual methods can be viewed as a generalized optimality criteria approach. The dual method is successfully extended to deal with pure discrete and mixed continuous-discrete design variable problems. The power of the method presented is illustrated with numerical results for example problems, including a metallic swept wing and a thin delta wing with fiber composite skins
Stability and Error Analysis for Optimization and Generalized Equations
Stability and error analysis remain challenging for problems that lack
regularity properties near solutions, are subject to large perturbations, and
might be infinite dimensional. We consider nonconvex optimization and
generalized equations defined on metric spaces and develop bounds on solution
errors using the truncated Hausdorff distance applied to graphs and epigraphs
of the underlying set-valued mappings and functions. In the process, we extend
the calculus of such distances to cover compositions and other constructions
that arise in nonconvex problems. The results are applied to constrained
problems with feasible sets that might have empty interiors, solution of KKT
systems, and optimality conditions for difference-of-convex functions and
composite functions
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