Méthode du sous-gradient réduit généralisé comme extension du GRG d'Abadie au cas non différentiable
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Displaying 1 – 13 of 13
Metric subregularity for nonclosed convex multifunctions in normed spaces
Xi Yin Zheng, Kung Fu Ng (2010)
ESAIM: Control, Optimisation and Calculus of Variations
In terms of the normal cone and the coderivative, we provide some necessary and/or sufficient conditions of metric subregularity for (not necessarily closed) convex multifunctions in normed spaces. As applications, we present some error bound results for (not necessarily lower semicontinuous) convex functions on normed spaces. These results improve and extend some existing error bound results.
Minimal invasion: An optimal L∞ state constraint problem
Christian Clason, Kazufumi Ito, Karl Kunisch (2011)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
In this work, the least pointwise upper and/or lower bounds on the state variable on a specified subdomain of a control system under piecewise constant control action are sought. This results in a non-smooth optimization problem in function spaces. Introducing a Moreau-Yosida regularization of the state constraints, the problem can be solved using a superlinearly convergent semi-smooth Newton method. Optimality conditions are derived, convergence of the Moreau-Yosida regularization is proved, and...
Minimal invasion: An optimal L∞ state constraint problem
Christian Clason, Kazufumi Ito, Karl Kunisch (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
In this work, the least pointwise upper and/or lower bounds on the state variable on a specified subdomain of a control system under piecewise constant control action are sought. This results in a non-smooth optimization problem in function spaces. Introducing a Moreau-Yosida regularization of the state constraints, the problem can be solved using a superlinearly convergent semi-smooth Newton method. Optimality conditions are derived, convergence of the Moreau-Yosida regularization is proved, and...
Minimal pairs representing selections of four linear functions in .
Grzybowski, J., Pallaschke, D., Urbański, R. (2000)
Journal of Convex Analysis
Minimization of nonsmooth convex functionals in Banach spaces.
Alber, Ya.I., Iusem, A.N., Solodov, M.V. (1997)
Journal of Convex Analysis
Minimization of nonsmooth integral functionals.
Papageorgiou, Nikolaos S., Papageorgiou, Apostolos S. (1992)
International Journal of Mathematics and Mathematical Sciences
Monotone trajectories of dynamical systems and Clarke's generalized Jacobian.
Crespi, Giovanni P., Rocca, Matteo (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Monotonicity and differential properties of the value functions in optimal control.
Mirică, Ştefan (2004)
International Journal of Mathematics and Mathematical Sciences
More than first-order developments of convex functions: primal-dual relations.
Lemaréchal, C., Sagastizábel, C. (1996)
Journal of Convex Analysis
Moreau's decomposition theorem revisited
J. B. Hiriart-Urruty, Ph. Plazanet (1989)
Annales de l'I.H.P. Analyse non linéaire
Multiple solutions for a singular semilinear elliptic problems with critical exponent and symmetries.
Cano, Alfredo, Hernández-Linares, Sergio, Hernández-Martínez, Eric (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Multivalued backward stochastic differential equations with time delayed generators
Bakarime Diomande, Lucian Maticiuc (2014)
Open Mathematics
Our aim is to study the following new type of multivalued backward stochastic differential equation: where ∂φ is the subdifferential of a convex function and (Y t, Z t):= (Y(t + θ), Z(t + θ))θ∈[−T,0] represent the past values of the solution over the interval [0, t]. Our results are based on the existence theorem from Delong Imkeller, Ann. Appl. Probab., 2010, concerning backward stochastic differential equations with time delayed generators.
Currently displaying 1 – 13 of 13
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