The maximum principle in optimal control, then and now
In the paper we investigate the regularity of the value function representing Hamilton–Jacobi equation: − Ut + H(t, x, U, − Ux) = 0 with a final condition: U(T,x) = g(x). Hamilton–Jacobi equation, in which the Hamiltonian H depends on the value of solution U, is represented by the value function with more complicated structure than the value function in Bolza problem. This function is described with the use of some class of Mayer problems related to the optimal control theory and the calculus of...
The paper concerns the study of tilt stability of local minimizers in standard problems of nonlinear programming. This notion plays an important role in both theoretical and numerical aspects of optimization and has drawn a lot of attention in optimization theory and its applications, especially in recent years. Under the classical Mangasarian-Fromovitz Constraint Qualification, we establish relationships between tilt stability and some other stability notions in constrained optimization. Involving...
We consider an elliptic boundary value problem with unilateral constraints and subdifferential boundary conditions. The problem describes the heat transfer in a domain and its weak formulation is in the form of a hemivariational inequality for the temperature field, denoted by . We associate to Problem an optimal control problem, denoted by . Then, using appropriate Tykhonov triples, governed by a nonlinear operator and a convex , we provide results concerning the well-posedness of problems...
Mediante el uso de una generalización de los subgradientes, se demuestra una condición dual de optimalidad necesaria y suficiente para Optimización Convexa. No se requiere la cualificación de restricciones en el caso finito-dimensional.
Under an appropriate oscillating behaviour either at zero or at infinity of the nonlinear term, the existence of a sequence of weak solutions for an eigenvalue Dirichlet problem on the Sierpiński gasket is proved. Our approach is based on variational methods and on some analytic and geometrical properties of the Sierpiński fractal. The abstract results are illustrated by explicit examples.
2000 Mathematics Subject Classification: 49J40, 49J35, 58E30, 47H05We establish variational principles for monotone and maximal bifunctions of Brøndsted-Rockafellar type by using our characterization of bifunction’s maximality in reflexive Banach spaces. As applications, we give an existence result of saddle point for convex-concave function and solve an approximate inclusion governed by a maximal monotone operator.
The aim of this paper is to summarize basic facts about -stable at a point vector functions and existing results for certain vector constrained programming problem with -stable data.