Robert Wenczel

Some Sufficient Optimality Conditions in Nonsmooth Analysis

In this paper we study some second order conditions that may be added to the first order nessessary optimality condition

Convergence of truncates in l1 optimal feedback control 61

0\in\partial_{p}f(\bar{x})

Slice Convergence of Sums of Convex functions in Banach Spaces and Saddle Point Convergence

(with

A study of tilt-stable optimality and sufficient conditions

\partial_{p}f

On the Variational Behaviour of the Subhessians of the Lasry-Lions Envelope £

denoting the proximal subdifferential) in order to obtain a sufficient condition for a strict local minimum for extended-real-valued, nonsmooth functions. Three different types of second order conditions are investigated, all based on a different second order subdifferential. Namely, the subhessian, the graphical derivative, and the (contingent) coderivative to the proximal subdifferential.

On the Calculus of Limiting Subhessians

Existing design methodologies based on infinite-dimensional linear programming generally require an iterative process often involving progressive increase of truncation length, in order to achieve a desired accuracy. In this chapter we consider the fundamental problem of determining a priori estimates of the truncation length sufficient for attainment of a given accuracy in the optimal objective value of certain infinite-dimensional linear programs arising in optimal feedback control. The treatment here also allows us to consider objective functions lacking interiority of domain, a problem which often arises in practice.

All Maximal Monotone Operators in a Banach Space are of Type FPV

In this note we provide various conditions under which the slice convergence of f v → f and g v → g implies that of f v + g v to f + g, where f v veW and g v veW are parametrized families of closed, proper, convex function in a general Banach space X. This’ sum theorem’ complements a result found in [EW00] for the epidistance convergence of sums. It also provides an alternative approach to the derivation of some of the results recently proved in [Zal03] for slice convergence in the case when the spaces are Banach spaces. We apply these results to the problem of convergence of saddle points associated with Fenchel duality of slice convergent families of functions.