Displaying similar documents to “Using geometric constraints to capture design intent.”

Abstract variational problems with volume constraints

Marc Oliver Rieger (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Existence results for a class of one-dimensional abstract variational problems with volume constraints are established. The main assumptions on their energy are additivity, translation invariance and solvability of a transition problem. These general results yield existence results for nonconvex problems. A counterexample shows that a naive extension to higher dimensional situations in general fails.

A Survey on Vector Variational Inequalities

F. Giannessi, G. Matroeni, X. Q. Yang (2009)

Bollettino dell'Unione Matematica Italiana

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The paper consists in a brief overview on Vector Variational Inequalities (VVI). The connections between VVI and Vector Optimization Problems (VOP) are considered. This leads to point out that necessary optimality conditions for a VOP can be formulated by means of a VVI when the objective function is Gâteaux differentiable and the feasible set is convex. In particular, the existence of solutions and gap functions associated with VVI are analysed. Gap functions provide an equivalent formulation...

Conical differentiability for bone remodeling contact rod models

Isabel N. Figueiredo, Carlos F. Leal, Cecília S. Pinto (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove the conical differentiability of the solution to a bone remodeling contact rod model, for given data (applied loads and rigid obstacle), with respect to small perturbations of the cross section of the rod. The proof is based on the special structure of the model, composed of a variational inequality coupled with an ordinary differential equation with respect to time. This structure enables the verification of the two following fundamental results: the polyhedricity of a modified...

A note on Minty type vector variational inequalities

Giovanni P. Crespi, Ivan Ginchev, Matteo Rocca (2006)

RAIRO - Operations Research

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The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space ...