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Displaying 401 –
420 of
4417
In the sub-Riemannian framework, we give geometric necessary and sufficient conditions for the existence of abnormal extremals of the Maximum Principle. We give relations between abnormality, -rigidity and length minimizing. In particular, in the case of three dimensional manifolds we show that, if there exist abnormal extremals, generically, they are locally length minimizing and in the case of four dimensional manifolds we exhibit abnormal extremals which are not -rigid and which can be minimizing...
It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to the addition of boundary terms to the action, as it happens instead when the correct procedure is applied. Examples are considered to show how leaving derivatives of fields unconstrained affects the physical interpretation of the model. This is justified in particular...
We discuss the stability of "critical" or "equilibrium" shapes of
a shape-dependent energy functional. We analyze a problem arising when
looking at the positivity of the second derivative in order to prove
that a critical shape is an optimal shape. Indeed, often when
positivity -or coercivity- holds, it does for a weaker norm than the
norm for which the functional is twice differentiable and local
optimality cannot be a priori deduced. We solve this problem for a
particular but significant example....
The relation between the general optimality conditions in terms of contact cones and the Kuhn-Tucker conditions in the special case of pseudo-convex and quasi-convex functions and their consequence to Lagrangian multipliers are given.
A class of quasi-variational inequalities (QVI) of elliptic type is studied in reflexive Banach spaces. The concept of QVI was earlier introduced by A. Bensoussan and J.-L. Lions [2] and its general theory has been developed by many mathematicians, for instance, see [6, 7, 9, 13] and a monograph [1]. In this paper we give a generalization of the existence theorem established in [14]. In our treatment we employ the compactness method along with a concept of convergence of nonlinear multivalued operators...
∗ The work is partially supported by NSFR Grant No MM 409/94.We develop an abstract subdifferential calculus for lower
semicontinuous functions and investigate functions similar to convex functions.
As application we give sufficient conditions for the integrability of a lower
semicontinuous function.
Recently, we established some generalizations of the theory of Lagrange multipliers arising from nonlinear programming in Banach spaces, which enable us to treat not only elliptic problems but also parabolic problems in the same generalized framework. The main objective of the present paper is to discuss a typical time-dependent double obstacle problem as a new application of the above mentioned generalization. Actually, we describe it as a usual parabolic variational inequality and then characterize...
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.
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.
The optimal experiment for estimating the parameters of a nonlinear regression model usually depends on the value of these parameters, hence the problem of designing experiments that are robust with respect to parameter uncertainty. Sequential designpermits to adapt the experiment to the value of the parameters, and can thus be considered as a robust design procedure. By designing theexperiments sequentially, one introduces a feedback of information, and thus dynamics, into the design procedure....
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution...
Currently displaying 401 –
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4417