Search results for "Subderivative"

Approximations and Metric Regularity in Mathematical Programming in Banach Space

1993

This paper establishes verifiable conditions ensuring the important notion of metric regularity for general nondifferentiable programming problems in Banach spaces. These conditions are used to obtain Lagrange-Kuhn-Tucker multipliers for minimization problems with infinitely many inequality and equality constraints.

About the finite convergence of the proximal point algorithm

1988

We study the finite convergence property of the proximal point algorithm applied to the partial inverse, with respect to a subspace, of the subdifferential of a polyhedral convex function. Using examples we show how sufficient conditions providing the finite convergence can be realized and we give a case with non finite termination.

An implicit non-linear time dependent equation has a solution

1991

has a solution (u, u, w). The operators &s(l) and a(t) are maximal monotone from a real Hilbert space V to its dual such that &(r) + 9?(r) are V-coercive and a(r) are not degenerate. A linear compact injection i embeds V to a real Banach space W and each d(r) is the strongly monotone subdifferential of a continuous convex function #(I, ) on W. The function f is square integrable. The functions W(r): V+ W* are Lipschitzian as V*-valued functions. Section 3 contains the theorems. The main result is Theorem 2. Theorems 3 and 4 demonstrate the smoothing effect on the initial condition. Their proofs are given in Section 4. They exploit the methods of di Benedetto and Showalter, [4], who studied …

Coderivatives of multivalued mappings, locally compact cones and metric regularity

1999

On a class of compactly epi-Lipschitzian sets

2003

The paper is devoted to the study of the so-called compactly epi-Lipschitzian sets. These sets are needed for many aspects of generalized differentiation, particulary for necessary optimality conditions, stability of mathematical programming problems and calculus rules for subdifferentials and normal cones. We present general conditions under which sets defined by general constraints are compactly epi-Lipschitzian. This allows us to show how the compact epi-Lipschitzness properties behave under set intersections.

C 1,ω (·) -regularity and Lipschitz-like properties of subdifferential

2012

Characterizations of convex approximate subdifferential calculus in Banach spaces

2016

International audience; We establish subdifferential calculus rules for the sum of convex functions defined on normed spaces. This is achieved by means of a condition relying on the continuity behaviour of the inf-convolution of their corresponding conjugates, with respect to any given topology intermediate between the norm and the weak* topologies on the dual space. Such a condition turns out to also be necessary in Banach spaces. These results extend both the classical formulas by Hiriart-Urruty and Phelps and by Thibault.