Optimization of Convex function on w*-compact sets.
Consideriamo un corpo sottomesso ad una forza esterna data e del quale vogliamo controllare lo spostamento. Cerchiamo un rinforzo per minimizzare un funzionale che dipende dallo spostamento del corpo. L'insieme delle configurazioni ammissibili è un insieme di funzioni caratteristiche di sottodomini (un rinforzo ammissibile è un sottodominio con una rigidezza uguale ad uno) di volume prescritto. In tal caso, si ha bisogno di una versione rilassata del problema di ottimizzazione e si cerca una densità...
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 for a bilinear...
With reference to the work of Verriest and Lewis (1991) on continuous finite-dimensional systems, the linear quadratic minimum-time problem is considered for discrete distributed systems and discrete distributed time delay systems. We treat the problem in two variants, with fixed and free end points. We consider a cost functional J which includes time, energy and precision terms, and then we investigate the optimal pair (N, u) which minimizes J.
The purpose of the paper is to discuss the applicability of stochastic programming models and methods to civil engineering design problems. In cooperation with experts in civil engineering, the problem concerning an optimal design of beam dimensions has been chosen. The corresponding mathematical model involves an ODE-type constraint, uncertain parameter related to the material characteristics and multiple criteria. As a~result, a~multi-criteria stochastic nonlinear optimization model is obtained....
DiPerna's and Majda's generalization of Young measures is used to describe oscillations and concentrations in sequences of maps satisfying a linear differential constraint . Applications to sequential weak lower semicontinuity of integral functionals on -free sequences and to weak continuity of determinants are given. In particular, we state necessary and sufficient conditions for weak* convergence of det in measures on the closure of if in . This convergence holds, for example, under...