-valued maps minimizing the norm of the gradient with free discontinuities
Saddle point criteria for second order -approximated vector optimization problems
The purpose of this paper is to apply second order -approximation method introduced to optimization theory by Antczak [2] to obtain a new second order -saddle point criteria for vector optimization problems involving second order invex functions. Therefore, a second order -saddle point and the second order -Lagrange function are defined for the second order -approximated vector optimization problem constructed in this approach. Then, the equivalence between an (weak) efficient solution of the...
Saddle point theorems on generalized convex spaces.
Saddle Points and Multiple Solutions of Differential Equations.
Saddle-point problems in partial differential equations and applications to linear quadratic differential games
Scaling laws for non-euclidean plates and the isometric immersions of riemannian metrics
Recall that a smooth Riemannian metric on a simply connected domain can be realized as the pull-back metric of an orientation preserving deformation if and only if the associated Riemann curvature tensor vanishes identically. When this condition fails, one seeks a deformation yielding the closest metric realization. We set up a variational formulation of this problem by introducing the non-Euclidean version of the nonlinear elasticity functional, and establish its Γ-convergence under the proper...
Scaling laws for non-Euclidean plates and the W2,2 isometric immersions of Riemannian metrics
Recall that a smooth Riemannian metric on a simply connected domain can be realized as the pull-back metric of an orientation preserving deformation if and only if the associated Riemann curvature tensor vanishes identically. When this condition fails, one seeks a deformation yielding the closest metric realization. We set up a variational formulation of this problem by introducing the non-Euclidean version of the nonlinear elasticity functional, and establish its Γ-convergence under the proper scaling....
s-coincidence and s-common fixed point theorems for two pairs of set-valued noncompatible mappings in two pairs of set-valued noncompatible mappings in metric space.
Scope and generalization of the theory of linearly constrained linear regulator
A previous paper by the same authors presented a general theory solving (finite horizon) feasibility and optimization problems for linear dynamic discrete-time systems with polyhedral constraints. We derived necessary and sufficient conditions for the existence of solutions without assuming any restrictive hypothesis. For the solvable cases we also provided the inequative feedback dynamic system, that generates by forward recursion all and nothing but the feasible (or optimal, according to the cases)...
Scorza-Dragoni's Theorem for Unbounded Set-Valued Functions and its Applications to Control Problems
SDP approach for solving LQ control problem subject to implicit system.
Second order conditions for bang-bang control problems
Second order conditions for extrema of functionals defined on regular surfaces.
Second order conditions for periodic optimal control problems
Second order conditions in optimal control problems with mixed equality-type constraints on a variable time interval
Second order differentiability and Lipschitz smooth points of convex functionals
Second order differentiability of integral functionals on Sobolev spaces and L2-spaces.
Second order information on Palais-smale sequences in the mountain pass theorem.
Second order optimality conditions in the smooth case and applications in optimal control
The aim of this article is to present algorithms to compute the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal. It is based on recent theoretical developments of geometric optimal control, and the article contains a review of second order optimality conditions. The computations are related to a test of positivity of the intrinsic second order derivative or a test of singularity of the extremal flow. We derive an algorithm called COTCOT (Conditions...
Second order unbounded parabolic equations in separated form
We prove existence and uniqueness of viscosity solutions of Cauchy problems for fully nonlinear unbounded second order Hamilton-Jacobi-Bellman-Isaacs equations defined on the product of two infinite-dimensional Hilbert spaces H'× H'', where H'' is separable. The equations have a special "separated" form in the sense that the terms involving second derivatives are everywhere defined, continuous and depend only on derivatives with respect to x'' ∈ H'', while the unbounded terms are of first order...