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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...
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...
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...
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...
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...
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...
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.
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.
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.
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].
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126