On a method of optimization
On an infinite dimensional linear-quadratic problem with fixed endpoints: the continuity question
In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study the continuity of minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.
On distributed parameter control systems in the abnormal case and in the case of nonoperator equality constraints.
On localizing global Pareto solutions in a given convex set
Sufficient conditions are given for the global Pareto solution of the multicriterial optimization problem to be in a given convex subset of the domain. In the case of maximizing real valued-functions, the conditions are sufficient and necessary without any convexity type assumptions imposed on the function. In the case of linearly scalarized vector-valued functions the conditions are sufficient and necessary provided that both the function is concave and the scalarization is increasing with respect...
On necessary optimality conditions in a class of optimization problems
In the paper necessary optimality conditions are derived for the minimization of a locally Lipschitz objective with respect to the consttraints , where is a closed set and is a set-valued map. No convexity requirements are imposed on . The conditions are applied to a generalized mathematical programming problem and to an abstract finite-dimensional optimal control problem.
On some general almost periodic optimal control problems : links with periodic problems and necessary conditions
In this paper, we are concerned with periodic, quasi-periodic (q.p.) and almost periodic (a.p.) Optimal Control problems. After defining these problems and setting them in an abstract setting by using Abstract Harmonic Analysis, we give some structure results of the set of solutions, and study the relations between periodic and a.p. problems. We prove for instance that for an autonomous concave problem, the a.p. problem has a solution if and only if all problems (periodic with fixed or variable...
On some general almost periodic Optimal Control problems: links with periodic problems and necessary conditions
In this paper, we are concerned with periodic, quasi-periodic (q.p.) and almost periodic (a.p.) Optimal Control problems. After defining these problems and setting them in an abstract setting by using Abstract Harmonic Analysis, we give some structure results of the set of solutions, and study the relations between periodic and a.p. problems. We prove for instance that for an autonomous concave problem, the a.p. problem has a solution if and only if all problems (periodic with fixed or variable...
On some structural design problems
On the Accuracy of Regularized Solutions to Quadratic Minimization Problems on a Half-Space, in Case of a Normally Solvable Operator
On the characteristic properties of certain optimization problems in complex analysis
We shall be concerned in this paper with an optimization problem of the form: J(f) → min(max) subject to f ∈ 𝓕 where 𝓕 is some family of complex functions that are analytic in the unit disc. For this problem, the question about its characteristic properties is considered. The possibilities of applications of the results of general optimization theory to such a problem are also examined.
On the isoperimetric-type problems with current hyperplanes.
On the maximum principle for optimal control processes described by Hammerstein integral equations with weakly singular kernels
On the measurability of the conjugate and the subdifferential of a normal integrand.
On the minimum time control problem and continuous families of convex sets
On the Variational Characterization of Bivariate Interpolation Methods.
Optimal control of delay-differential inclusions with multivalued initial conditions in infinite dimensions
Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations
In this paper, we consider optimal feedback control for stochastc infinite dimensional systems. We present some new results on the solution of associated HJB equations in infinite dimensional Hilbert spaces. In the process, we have also developed some new mathematical tools involving distributions on Hilbert spaces which may have many other interesting applications in other fields. We conclude with an application to optimal stationary feedback control.
Optimal control of nonlinear evolution equations
In this paper, first we consider parametric control systems driven by nonlinear evolution equations defined on an evolution triple of spaces. The parametres are time-varying probability measures (Young measures) defined on a compact metric space. The appropriate optimization problem is a minimax control problem, in which the system analyst minimizes the maximum cost (risk). Under general hypotheses on the data we establish the existence of optimal controls. Then we pass to nonparametric...
Optimal control of semilinear evolution inclusions via discrete approximations
Optimal controls for distributed parameter systems with mixed constraints