15,228 research outputs found
The infinite dimensional Lagrange multiplier rule for convex optimization problems
AbstractIn this paper an infinite dimensional generalized Lagrange multipliers rule for convex optimization problems is presented and necessary and sufficient optimality conditions are given in order to guarantee the strong duality. Furthermore, an application is presented, in particular the existence of Lagrange multipliers associated to the bi-obstacle problem is obtained
Structural optimization of large structural systems by optimality criteria methods
The fundamental concepts of the optimality criteria method of structural optimization are presented. The effect of the separability properties of the objective and constraint functions on the optimality criteria expressions is emphasized. The single constraint case is treated first, followed by the multiple constraint case with a more complex evaluation of the Lagrange multipliers. Examples illustrate the efficiency of the method
Optimal bilinear control problem related to a chemo-repulsion system in 2D domains
In this paper we study a bilinear optimal control problem associated to a
chemo-repulsion model with linear production term. We analyze the existence,
uniqueness and regularity of pointwise strong solutions in a bidimensional
domain. We prove the existence of an optimal solution and, using a Lagrange
multipliers theorem, we derive first-order optimality conditions
An extension of Yuan's Lemma and its applications in optimization
We prove an extension of Yuan's Lemma to more than two matrices, as long as
the set of matrices has rank at most 2. This is used to generalize the main
result of [A. Baccari and A. Trad. On the classical necessary second-order
optimality conditions in the presence of equality and inequality constraints.
SIAM J. Opt., 15(2):394--408, 2005], where the classical necessary second-order
optimality condition is proved under the assumption that the set of Lagrange
multipliers is a bounded line segment. We prove the result under the more
general assumption that the hessian of the Lagrangian evaluated at the vertices
of the Lagrange multiplier set is a matrix set with at most rank 2. We apply
the results to prove the classical second-order optimality condition to
problems with quadratic constraints and without constant rank of the jacobian
matrix
Optimal control of obstacle problems : existence of Lagrange multipliers
We study first order optimality systems for the control of a system governed by a variational inequality and deal with Lagrange multipliers : is it possible to associate to each pointwise constraint a multiplier to get a ``good'' optimality system ? We give positive and negative answers for the finite and infinite dimensional cases. These results are compared with the previous ones got by penalization or differentiation
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