Search results for "Mathematics::Optimization and Control"
showing 10 items of 30 documents
More indefinite integrals from Riccati equations
2019
ABSTRACTTwo new methods for obtaining indefinite integrals of a special function using Riccati equations are presented. One method uses quadratic fragments of the Riccati equation, the solutions of...
Solving coupled Riccati matrix differential systems
1991
Abstract We start by noting that coupled Riccati matrix differential systems appearing in differential games may be considered as a single rectangular Riccati equation. An explicit solution of the coupled differential system in terms of a solution of the associated algebraic Riccati equation is given.
On the Calmness of a Class of Multifunctions
2002
The paper deals with the calmness of a class of multifunctions in finite dimensions. Its first part is devoted to various conditions for calmness, which are derived in terms of coderivatives and subdifferentials. The second part demonstrates the importance of calmness in several areas of nonsmooth analysis. In particular, we focus on nonsmooth calculus and solution stability in mathematical programming and in equilibrium problems. The derived conditions find a number of applications there.
Cotype 2 estimates for spaces of polynomials on sequence spaces
2002
We give asymptotically correct estimations for the cotype 2 constant C2(P(mXn)) ofthe spaceP(mXn) of allm-homogenous polynomials onXn, the span of the firstn sequencesek=(\gdkj)j in a Banach sequence spaceX. Applications to Minkowski, Orlicz and Lorentz sequence spaces are given.
An Adaptive Alternating Direction Method of Multipliers
2021
AbstractThe alternating direction method of multipliers (ADMM) is a powerful splitting algorithm for linearly constrained convex optimization problems. In view of its popularity and applicability, a growing attention is drawn toward the ADMM in nonconvex settings. Recent studies of minimization problems for nonconvex functions include various combinations of assumptions on the objective function including, in particular, a Lipschitz gradient assumption. We consider the case where the objective is the sum of a strongly convex function and a weakly convex function. To this end, we present and study an adaptive version of the ADMM which incorporates generalized notions of convexity and penalty…
An eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities
2005
AbstractA multiplicity result for an eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities is obtained. The proof is based on a three critical points theorem for nondifferentiable functionals.
Weak regularity of functions and sets in Asplund spaces
2006
Abstract In this paper, we study a new concept of weak regularity of functions and sets in Asplund spaces. We show that this notion includes prox-regular functions, functions whose subdifferential is weakly submonotone and amenable functions in infinite dimension. We establish also that weak regularity is equivalent to Mordukhovich regularity in finite dimension. Finally, we give characterizations of the weak regularity of epi-Lipschitzian sets in terms of their local representations.
The Fixed Point Property in Banach Spaces with the NUS-Property
1997
Abstract In this paper, we show that the weak nearly uniform smooth Banach spaces have the fixed point property for nonexpansive mappings.
Fixed point theory for a class of generalized nonexpansive mappings
2011
AbstractIn this paper we introduce two new classes of generalized nonexpansive mapping and we study both the existence of fixed points and their asymptotic behavior.
Closedness and lower semicontinuity of positive sesquilinear forms
2009
The relationship between the notion of closedness, lower semicontinuity and completeness (of a quotient) of the domain of a positive sesquilinear form defined on a subspace of a topological vector space is investigated and sufficient conditions for their equivalence are given.