-monotonicity and applications to nonlinear variational inclusion problems.
A moving mesh fictitious domain approach for shape optimization problems
A moving mesh fictitious domain approach for shape optimization problems
A new numerical method based on fictitious domain methods for shape optimization problems governed by the Poisson equation is proposed. The basic idea is to combine the boundary variation technique, in which the mesh is moving during the optimization, and efficient fictitious domain preconditioning in the solution of the (adjoint) state equations. Neumann boundary value problems are solved using an algebraic fictitious domain method. A mixed formulation based on boundary Lagrange multipliers is...
A multidimensional singular stochastic control problem on a finite time horizon
A singular stochastic control problem in n dimensions with timedependent coefficients on a finite time horizon is considered. We show that the value function for this problem is a generalized solution of the corresponding HJB equation with locally bounded second derivatives with respect to the space variables and the first derivative with respect to time. Moreover, we prove that an optimal control exists and is unique
A multiscale correction method for local singular perturbations of the boundary
In this work, we consider singular perturbations of the boundary of a smooth domain. We describe the asymptotic behavior of the solution uE of a second order elliptic equation posed in the perturbed domain with respect to the size parameter ε of the deformation. We are also interested in the variations of the energy functional. We propose a numerical method for the approximation of uE based on a multiscale superposition of the unperturbed solution u0 and a profile defined in a model domain. We...
A necessity measure optimization approach to linear programming problems with oblique fuzzy vectors
In this paper, a necessity measure optimization model of linear programming problems with fuzzy oblique vectors is discussed. It is shown that the problems are reduced to linear fractional programming problems. Utilizing a special structure of the reduced problem, we propose a solution algorithm based on Bender’s decomposition. A numerical example is given.
A new approach for simultaneous shape and topology optimization based on dynamic implicit surface function
A new approach for simultaneous shape and topology optimization based on dynamic implicit surface function
A new approach to the constrained controllability problem
We consider the problem of internal regional controllability with output constraints. It consists in steering a hyperbolic system to a final state between two prescribed functions only on a subregion of the evolution system domain. This problem is solved by characterizing the optimal control in terms of a subdifferential associated with the minimized functional.
A new approach to the extragradient method for nonlinear variational inequalities.
A new approach to Young measure theory, relaxation and convergence in energy
A new approximation method for solving variational inequalities and fixed points of nonexpansive mappings.
A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations
A new iterative algorithm for the set of fixed-point problems of nonexpansive mappings and the set of equilibrium problem and variational inequality problem.
A new method for nonsmooth convex optimization.
A new method for obtaining eigenvalues of variational inequalities: operators with multiple eigenvalues
A new method for solving monotone generalized variational inequalities.
A new method for the obtaining of eigenvalues of variational inequalities of the special type (Preliminary communication)
A new method of proof of Filippov’s theorem based on the viability theorem
Filippov’s theorem implies that, given an absolutely continuous function y: [t 0; T] → ℝd and a set-valued map F(t, x) measurable in t and l(t)-Lipschitz in x, for any initial condition x 0, there exists a solution x(·) to the differential inclusion x′(t) ∈ F(t, x(t)) starting from x 0 at the time t 0 and satisfying the estimation where the function γ(·) is the estimation of dist(y′(t), F(t, y(t))) ≤ γ(t). Setting P(t) = x ∈ ℝn: |x −y(t)| ≤ r(t), we may formulate the conclusion in Filippov’s theorem...
A new minimal point theorem in product spaces.