Saddle-point problems in partial differential equations and applications to linear quadratic differential games
Separation theorems for sets in product spaces and equivalent assertions
Singolarità di funzioni semiconcave ed applicazioni al controllo ottimo
Solvability and numerical algorithms for a class of variational data assimilation problems
A class of variational data assimilation problems on reconstructing the initial-value functions is considered for the models governed by quasilinear evolution equations. The optimality system is reduced to the equation for the control function. The properties of the control equation are studied and the solvability theorems are proved for linear and quasilinear data assimilation problems. The iterative algorithms for solving the problem are formulated and justified.
Solvability and numerical algorithms for a class of variational data assimilation problems
A class of variational data assimilation problems on reconstructing the initial-value functions is considered for the models governed by quasilinear evolution equations. The optimality system is reduced to the equation for the control function. The properties of the control equation are studied and the solvability theorems are proved for linear and quasilinear data assimilation problems. The iterative algorithms for solving the problem are formulated and justified.
Solving the set equilibrium problems.
Some existence results on noncoercive variational inequalities
Some remarks on subdifferentiability of convex functions.
Some results for an optimal control problem with a semilinear state equation
We consider a quadratic control problem with a semilinear state equation depending on a small parameter . We show that the optimal control is a regular function of such parameter.
Stability of saddle point problems with penalty
Stability results for convergence of convex sets and functions in nonreflexive spaces.
Let Γ(X) be the convex proper lower semicontinuous functions on a normed linear space X. We show, subject to Rockafellar’s constraints qualifications, that the operations of sum, episum and restriction are continuous with respect to the slice topology that reduces to the topology of Mosco convergence for reflexive X. We show also when X is complete that the epigraphical difference is continuous. These results are applied to convergence of convex sets.
Stochastic diffrential equations on Banach spaces and their optimal feedback control
In this paper we consider stochastic differential equations on Banach spaces (not Hilbert). The system is semilinear and the principal operator generating a C₀-semigroup is perturbed by a class of bounded linear operators considered as feedback operators from an admissible set. We consider the corresponding family of measure valued functions and present sufficient conditions for weak compactness. Then we consider applications of this result to several interesting optimal feedback control problems....
Stochastic evolution equations on Hilbert spaces with partially observed relaxed controls and their necessary conditions of optimality
In this paper we consider the question of optimal control for a class of stochastic evolution equations on infinite dimensional Hilbert spaces with controls appearing in both the drift and the diffusion operators. We consider relaxed controls (measure valued random processes) and briefly present some results on the question of existence of mild solutions including their regularity followed by a result on existence of partially observed optimal relaxed controls. Then we develop the necessary conditions...
Strongly proper optimums and maximal optimization in multiobjective programming.
Study of an approximation process of time optimal control for fractional evolution systems in Banach spaces.
Suboptimal boundary controls for elliptic equation in critically perforated domain
Superlinear Elliptic Boundary Value Problems.
Support separation theorems and their applications to vector surrogate reverse duality
Sur la régularité de certaines fonctions aléatoires d'Ornstein-Uhlenbeck
Sur le minimum des fonctionnelles dans les espaces de Banach