The CIO, one of the fourteen university research institutes in mathematics in Spain, will host on September 2 the 9th International Seminar on Optimization and Variational Analysis. The event will take place throughout the morning in classrooms 0.1 and 0.2 of Torretamarit Building of the UMH and it’s aimed at researchers and students interested in the subject.

OVA9_ 9th International Seminar on Optimization and Variational Analysis September 2, 2019, Torretamarit Bldg. Center of Operations Research, Miguel Hernández University of Elche Program (1)

Abstract. In this talk we introduce the family of Lipschitz in the small functions defined on a metric space $X$, discuss their basic properties, and present a very recent uniform closure result of Beer and Garrido for continuous real-valued functions that are Lipschitz in the small when restricted to each member of a family of a subsets $\mathscr {B}$ of $X$ that are “shielded from closed sets”. From this single result, we can easily show: (1) the Lipschitz in the small functions are uniformly dense in the uniformly continuous functions; (2) the locally Lipschitz functions are uniformly dense in the continuous functions; (3) the bounded Lipschitz functions are uniformly dense in the bounded uniformly  continuous functions; (4) the functions that are Lipschitz on bounded sets are uniformly dense in the uniformly continuous functions that are bounded on bounded sets.

Abstract. Often, in PDE constrained optimization the initial conditions are not known exactly but can rather be understood as being random. The application of some control to the system then also leads to random terminal states. Therefore, it is of much interest to find an optimal control such that the terminal state falls into some specified region at least with some specified probability. This optimization problem is an instance of probabilistic programming, where random inequalities are formulated as chance constraints. It will be analyzed and illustrated for the example of Neumann boundary control of the vibrating string.

Abstract. In this lecture we consider mathematical problems with complementarity constraints (MPCC). Under an appropriate constraint qualification we present an algebraic characterization for the strong stability of C-stationary points for MPCCs. The concept of strong stability was introduced by Kojima in 1980 for stationary points of standard nonlinear optimization programs; it refers to uniqueness and existence of stationary points where perturbations up to second order are allowed. This lecture generalizes this concept and its algebraic characterization to the context of MPCC.

  •  11:45 – 12:15 Coffee break

Abstract. This talk mainly focuses on the SQP method for conic programming. We establish the primal-dual superlinear convergence of the basic SQP method when the second-order sufficient condition holds, the multiplier mapping is calm, and the set of Lagrange multipliers is a singleton.Then we discuss superlinear convergence of quasi-Newton SQP methods via the Dennis-More condition for constrained optimization problems. Based on joint work with Ebrahim Sarabi (Miami University, OH, USA).

Abstract. In this talk we present a characterization of the Hölder calmness of the optimal set mapping in convex semi-infinite optimization. It is derived from the equivalence of this property with the Hölder calmness of certain lower-level set mapping. Some estimates of the modulus of Hölder calmness are also provided. The talk is based on the recent paper: A. Kruger, M.A. López, X. Yang and J. Zhu, Hölder Error Bounds and Hölder Calmness with Applications to Convex Semi-infinite Optimization, Set-Valued and Variational Analysis.