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A construction of a maximal monotone extension of a monotone map [PDF]
ESAIM: Proceedings and Surveys, 2007 A proof based on the axiom of choice shows that any monotone map has maximal mono- tone extensions but this proof is not constructive. In this paper, we give a construction of such an extension. The process is based on some density properties of (maximal) monotone maps given before. Resume. Afln de montrer qu'une multi-application monotone possµede une
Wilfredo Sosa, Jean-Pierre Crouzeix
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Relaxation methods for optimal control problems [PDF]
Bulletin of Mathematical Sciences, 2020 We consider a nonlinear optimal control problem with dynamics described by a differential inclusion involving a maximal monotone map A : ℝN → 2ℝN. We do not assume that D(A) = ℝN, incorporating in this way systems with unilateral constraints in our ...
Nikolaos S. Papageorgiou +2 more
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Identification of discontinuous parameters in double phase obstacle problems
Advances in Nonlinear Analysis, 2022 In this article, we investigate the inverse problem of identification of a discontinuous parameter and a discontinuous boundary datum to an elliptic inclusion problem involving a double phase differential operator, a multivalued convection term (a ...
Zeng Shengda +3 more
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Degree theory for the sum of VMO maps and maximal monotone maps [PDF]
Cubo, 2011 Let be an open bounded domain, a VMO map, and T : D(T) a maximal monotone map wit . We construct a degree for the sum of f + T, which can be viewed as a generalization of the degree both for VMO maps and maximal monotone maps.Sea un dominio abierto, un ...
Yuqing Chen +2 more
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Variational inequalities of perturbed maximal monotone mapping with applications
Applied Mathematics Letters, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huang, Yisheng, Zhou, Yuying
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Anti-periodic solutions for evolution equations associated with maximal monotone mappings
Applied Mathematics Letters, 2011 The authors consider the existence of anti-periodic solutions for differential inclusions in a real Hilbert space \(H\). The first result concerns the problem \[ x^{\prime }(t)\in -Ax(t)+f(t)\text{ a.e. on }\mathbb{R}, \] \[ x(t)=-x(t+T)\text{ for }t\in \mathbb{R}.
Juan J Nieto +2 more
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Optimal Design Versus Maximal Monge–Kantorovich Metrics [PDF]
Archive for Rational Mechanics and Analysis, 2021 The connection between the minimal elastic compliance problem and Monge transport involving the euclidean metric cost has been evidenced in the year 1997.
Karol Bołbotowski, G. Bouchitt'e
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Variance-Reduced Splitting Schemes for Monotone Stochastic Generalized Equations [PDF]
IEEE Transactions on Automatic Control, 2020 We consider monotone inclusion problems with expectation-valued operators, a class of problems that subsumes convex stochastic optimization problems with possibly smooth expectation-valued constraints as well as subclasses of stochastic variational ...
Shisheng Cui, U. Shanbhag
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Linear passive systems and maximal monotone mappings [PDF]
Mathematical Programming, 2015 The paper studies linear systems of the form \[ x'(t)=Ax(t)+Bz(t)+u(t),\quad w(t)=Cx(t)+Dz(t)\eqno (1) \] with \[ (-z(t),w(t))\in \operatorname{graph}(M), \] where \(M: {\mathbb R}^m\to {\mathcal P}({\mathbb R}^m)\) is a given maximal monotone map. The system (1) is equivalent with a differential inclusion of the form \[ x'(t)\in -H(x(t))+u(t).\eqno (2)
M. Kanat Camlibel +1 more
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A Proximal Point Algorithm for Finding a Common Zero of a Finite Family of Maximal Monotone Operators [PDF]
Sahand Communications in Mathematical Analysis, 2019 In this paper, we consider a proximal point algorithm for finding a common zero of a finite family of maximal monotone operators in real Hilbert spaces. Also, we give a necessary and sufficient condition for the common zero set of finite operators to be ...
Mohsen Tahernia +2 more
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