On subdifferentials of convex functions
On the Approximation of Hausdorff Upper Semi-Continuous Correspondences.
On the directional differentiability properties of the max-min function.
On the existence of viable solutions for a class of second order differential inclusions
We prove the existence of viable solutions to the Cauchy problem x” ∈ F(x,x’), x(0) = x₀, x’(0) = y₀, where F is a set-valued map defined on a locally compact set , contained in the Fréchet subdifferential of a ϕ-convex function of order two.
On the level sum of two convex functions on Banach spaces.
On the measurability of the conjugate and the subdifferential of a normal integrand.
On the open mapping principle and convex multivalued mappings
On the points of non-differentiability of convex functions
We characterize sets of non-differentiability points of convex functions on . This completes (in ) the result by Zajíček [2] which gives a characterization of the magnitude of these sets.
On the propagation of singularities of semi-convex functions
On the reduction of pairs of bounded closed convex sets
Let X be a Hausdorff topological vector space. For nonempty bounded closed convex sets A,B,C,D ⊂ X we denote by A ∔ B the closure of the algebraic sum A + B, and call the pairs (A,B) and (C,D) equivalent if A ∔ D = B ∔ C. We prove two main theorems on reduction of equivalent pairs. The first theorem implies that, in a finite-dimensional space, a pair of nonempty compact convex sets with a piecewise smooth boundary and parallel tangent spaces at some boundary points is not minimal. The second theorem...
On the set-valued calculus in problems of viability and control for dynamic processes : the evolution equation
On the singularities of convex functions.
On the solution set of nonconvex subdifferential evolution inclusions
On Uniform Differentiability
We introduce the notion of uniform Fréchet differentiability of mappings between Banach spaces, and we give some sufficient conditions for this property to hold.
On weak sharp minima for a special class of nonsmooth functions
We present a characterization of weak sharp local minimizers of order one for a function f: ℝⁿ → ℝ defined by , where the functions are strictly differentiable. It is given in terms of the gradients of and the Mordukhovich normal cone to a given set on which f is constant. Then we apply this result to a smooth nonlinear programming problem with constraints.
On weak solutions to a viscoelasticity model
On ε-optimal controls for state constraint problems
Open mapping theorem and inversion theorem for γ-paraconvex multivalued mappings and applications
We extend the open mapping theorem and inversion theorem of Robinson for convex multivalued mappings to γ-paraconvex multivalued mappings. Some questions posed by Rolewicz are also investigated. Our results are applied to obtain a generalization of the Farkas lemma for γ-paraconvex multivalued mappings.
Optimal control of constrained delay-differential inclusions with multivalued initial conditions
Optimal control of nonlinear evolution equations associated with time-dependent subdifferentials and applications
In this paper we consider optimal control problems for abstract nonlinear evolution equations associated with time-dependent subdifferentials in a real Hilbert space. We prove the existence of an optimal control that minimizes the nonlinear cost functional. Also, we study approximating control problems of our equations. Then, we show the relationship between the original optimal control problem and the approximating ones. Moreover, we give some applications of our abstract results.