All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 126

Showing per page

Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market∗

René Henrion, Jiří Outrata, Thomas Surowiec (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We consider an equilibrium problem with equilibrium constraints (EPEC) arising from the modeling of competition in an electricity spot market (under ISO regulation). For a characterization of equilibrium solutions, so-called M-stationarity conditions are derived. This first requires a structural analysis of the problem, e.g., verifying constraint qualifications. Second, the calmness property of a certain multifunction has to be verified in order...

Approximate maximum principle for discrete approximations of optimal control systems with nonsmooth objectives and endpoint constraints

Boris S. Mordukhovich, Ilya Shvartsman (2013)

ESAIM: Control, Optimisation and Calculus of Variations

The paper studies discrete/finite-difference approximations of optimal control problems governed by continuous-time dynamical systems with endpoint constraints. Finite-difference systems, considered as parametric control problems with the decreasing step of discretization, occupy an intermediate position between continuous-time and discrete-time (with fixed steps) control processes and play a significant role in both qualitative and numerical aspects of optimal control. In this paper we derive an...

Asymptotic analysis, existence and sensitivity results for a class of multivalued complementarity problems

Fabián Flores-Bazán, Rubén López (2006)

ESAIM: Control, Optimisation and Calculus of Variations

In this work we study the multivalued complementarity problem on the non-negative orthant. This is carried out by describing the asymptotic behavior of the sequence of approximate solutions to its multivalued variational inequality formulation. By introducing new classes of multifunctions we provide several existence (possibly allowing unbounded solution set), stability as well as sensitivity results which extend and generalize most of the existing ones in the literature. We also present some kind...

Characterizations of error bounds for lower semicontinuous functions on metric spaces

Dominique Azé, Jean-Noël Corvellec (2004)

ESAIM: Control, Optimisation and Calculus of Variations

Refining the variational method introduced in Azé et al. [Nonlinear Anal. 49 (2002) 643-670], we give characterizations of the existence of so-called global and local error bounds, for lower semicontinuous functions defined on complete metric spaces. We thus provide a systematic and synthetic approach to the subject, emphasizing the special case of convex functions defined on arbitrary Banach spaces (refining the abstract part of Azé and Corvellec [SIAM J. Optim. 12 (2002) 913-927], and the characterization...

Characterizations of error bounds for lower semicontinuous functions on metric spaces

Dominique Azé, Jean-Noël Corvellec (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Refining the variational method introduced in Azé et al. [Nonlinear Anal. 49 (2002) 643-670], we give characterizations of the existence of so-called global and local error bounds, for lower semicontinuous functions defined on complete metric spaces. We thus provide a systematic and synthetic approach to the subject, emphasizing the special case of convex functions defined on arbitrary Banach spaces (refining the abstract part of Azé and Corvellec [SIAM J. Optim. 12 (2002) 913-927], and the characterization...

Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators

Radu Ioan Boţ, Sorin-Mihai Grad (2011)

Open Mathematics

In this note we provide regularity conditions of closedness type which guarantee some surjectivity results concerning the sum of two maximal monotone operators by using representative functions. The first regularity condition we give guarantees the surjectivity of the monotone operator S(· + p) + T(·), where p ɛ X and S and T are maximal monotone operators on the reflexive Banach space X. Then, this is used to obtain sufficient conditions for the surjectivity of S + T and for the situation when...

Decomposable hulls of multifunctions

Andrzej Nowak, Celina Rom (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Let F be a multifunction with values in Lₚ(Ω, X). In this note, we study which regularity properties of F are preserved when we consider the decomposable hull of F.

Direct design of robustly asymptotically stabilizing hybrid feedback

Rafal Goebel, Andrew R. Teel (2009)

ESAIM: Control, Optimisation and Calculus of Variations

A direct construction of a stabilizing hybrid feedback that is robust to general measurement error is given for a general nonlinear control system that is asymptotically controllable to a compact set.

Ekeland's variational principle in locally p-convex spaces and related results

J. H. Qiu, S. Rolewicz (2008)

Studia Mathematica

In the framework of locally p-convex spaces, two versions of Ekeland's variational principle and two versions of Caristi's fixed point theorem are given. It is shown that the four results are mutually equivalent. Moreover, by using the local completeness theory, a p-drop theorem in locally p-convex spaces is proven.

Equilibrium of maximal monotone operator in a given set

Dariusz Zagrodny (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Sufficient conditions for an equilibrium of maximal monotone operator to be in a given set are provided. This partially answers to a question posed in [10].

Currently displaying 21 – 40 of 126