Moreau-Yosida Regularization of State-Dependent Sweeping Processes with Nonregular Sets

The existence and the convergence (up to a subsequence) of the Moreau-Yosida regularization for the state-dependent sweeping process with nonregular (subsmooth and positively alpha-far) sets are established. Then, by a reparametrization technique, the existence of solutions for bounded variation continuous state-dependent sweeping processes with nonregular (subsmooth and positively alpha-far) sets is proved. An application to vector hysteresis is discussed, where it is shown that the Play operator with positively alpha-far sets is well defined for bounded variation continuous inputs.     

Controllability and strong controllability of differential inclusions

In this paper, we prove sufficient conditions for controllability and strong controllability in terms of the Mordukhovich subdifferential for two classes of differential inclusions. The first one is the class of sub-Lipschitz multivalued functions introduced by Loewen-Rockafellar (1994) [10]. The second one, introduced recently by Clarke (2005) [18], is the class of multivalued functions which are pseudo-Lipschitz and satisfy the so-called tempered growth condition. To do this, we establish an error bound result in terms of the Mordukhovich subdifferential outside Asplund spaces.     

Tangency conditions for multivalued mappings

We prove that interiority conditions imply tangency conditions for two multivalued mappings from a topological space into a normed vector space. As a consequence, we obtain the lower semicontinuity of the intersection of two multivalued mappings. An application to the epi-upper semicontinuity of the sum of convex vector-valued mappings is given.     

Approximate subdifferential and metric regularity: The finite-dimensional case

The notion of graphical metric regularity is introduced and conditions ensuring this kind of regularity for systems of finite-dimensional multifunctions are given in terms of partial approximate subdifferentials.     

Metric regularity and second-order necessary optimality conditions for minimization problems under inclusion constraints

In this paper, we establish some general metric regularity results for multivalued functions on Banach spaces. Then, we apply them to derive second-order necessary optimality conditions for the problem of minimizing a functionf on the solution set of an inclusion 0F(x) withxC, whenF has a closed convex second-order derivative.The author is thankful to the referees for having helped him improve the quality of the paper.     

Chain rules for coderivatives of multivalued mappings in Banach spaces

Our basic object in this paper is to establish calculus rules for coderivatives of multivalued mappings between Banach spaces. We consider the coderivative which is associated to some geometrical approximate subdifferential for functions.

     

Subdifferentials of the Marginal Functions in Parametric Convex Optimization via Intersection Formulas

Journal of Optimization Theory and Applications - The aim of the present work is to use a metric intersection formula to estimate the subdifferential of the marginal function in the convex setting....     

Error Bounds for Eigenvalue and Semidefinite Matrix Inequality Systems

In this paper we give sufficient conditions for existence of error bounds for systems expressed in terms of eigenvalue functions (such as in eigenvalue optimization) or positive semidefiniteness (such as in semidefinite programming). The research of the author was partially supported by an NSERC grant.