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24
G.: An infeasible primaldual algorithm for total bounded variationbased infconvolutiontype image restoration
 J. Sci. Comput
, 2006
"... Abstract. In this paper, a primaldual algorithm for total bounded variation (TV)–type image restoration is analyzed and tested. Analytically it turns out that employing a global Lsregularization, with 1 < s ≤ 2, in the dual problem results in a local smoothing of the TVregularization term in t ..."
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Cited by 32 (8 self)
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Abstract. In this paper, a primaldual algorithm for total bounded variation (TV)–type image restoration is analyzed and tested. Analytically it turns out that employing a global Lsregularization, with 1 < s ≤ 2, in the dual problem results in a local smoothing of the TVregularization term in the primal problem. The local smoothing can alternatively be obtained as the infimal convolution of the rnorm, with r−1 + s−1 = 1, and a smooth function. In the case r = s = 2, this results in GaussTV–type image restoration. The globalized primaldual algorithm introduced in this paper works with generalized derivatives, converges locally at a superlinear rate, and is stable with respect to noise in the data. In addition, it utilizes a projection technique which reduces the size of the linear system that has to be solved per iteration. A comprehensive numerical study ends the paper. Key words. Fenchel duality, generalized Newtontype methods, image restoration, total bounded variation
Absolute stability and the LagrangeDirichlet theorem with monotone multivalued mappings
 Systems & Control Letters
, 2004
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On the performance of the particle swarm optimization algorithm with various Inertia Weight variants for computing optimal control of a class of hybrid systems”, Discrete Dynamics in Nature and Society
, 2006
"... This paper presents an alternative and efficient method for solving the optimal control of singlestage hybrid manufacturing systems which are composed with two different categories: continuous dynamics and discrete dynamics. Three different inertia weights, a constant inertia weight (CIW), timevar ..."
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Cited by 16 (0 self)
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This paper presents an alternative and efficient method for solving the optimal control of singlestage hybrid manufacturing systems which are composed with two different categories: continuous dynamics and discrete dynamics. Three different inertia weights, a constant inertia weight (CIW), timevarying inertia weight (TVIW), and globallocal best inertia weight (GLbestIW), are considered with the particle swarm optimization (PSO) algorithm to analyze the impact of inertia weight on the performance of PSO algorithm. The PSO algorithm is simulated individually with the three inertia weights separately to compute the optimal control of the singlestage hybrid manufacturing system, and it is observed that the PSO with the proposed inertia weight yields better result in terms of both optimal solution and faster convergence. Added to this, the optimal control problem is also solved through real coded genetic algorithm (RCGA) and the results are compared with the PSO algorithms. A typical numerical example is also included in this paper to illustrate the efficacy and betterment of the proposed algorithm. Several statistical analyses are carried out from which can be concluded that the proposed method is superior to all the other methods considered in this paper. Copyright © 2006 M. S. Arumugam and M. V. C. Rao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.
Semiconcavity results for optimal control problems admitting no singular minimizing controls
 Ann. Inst. H. Poincaré Non Linéaire
"... Abstract. Semiconcavity results have generally been obtained for optimal control problems in absence of state constraints. In this paper, we prove the semiconcavity of the value function of an optimal control problem with endpoint constraints for which all minimizing controls are supposed to be non ..."
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Cited by 13 (3 self)
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Abstract. Semiconcavity results have generally been obtained for optimal control problems in absence of state constraints. In this paper, we prove the semiconcavity of the value function of an optimal control problem with endpoint constraints for which all minimizing controls are supposed to be nonsingular. hal00862030, version 1 15 Sep 2013 1.
Exterior sphere condition and time optimal control for differential inclusions
 SIAM J. Control Optim
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Existence results for general inequality problems with constrains, Abstr
 Appl. Anal
"... This paper is concerned with existence results for inequality problems of type F0(u;v) +Ψ′(u;v) ≥ 0, for all v ∈ X, where X is a Banach space, F: X → R is locally Lipschitz, and Ψ: X → (−∞+∞] is proper, convex, and lower semicontinuous. Here F0 stands for the generalized directional derivative of ..."
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Cited by 2 (1 self)
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This paper is concerned with existence results for inequality problems of type F0(u;v) +Ψ′(u;v) ≥ 0, for all v ∈ X, where X is a Banach space, F: X → R is locally Lipschitz, and Ψ: X → (−∞+∞] is proper, convex, and lower semicontinuous. Here F0 stands for the generalized directional derivative of F and Ψ′ denotes the directional derivative of Ψ. The applications we consider focus on the variationalhemivariational inequalities involving the pLaplacian operator. 1.
Existence of Solutions for Nonconvex and Nonsmooth Vector Optimization Problems
, 2008
"... We consider the weakly efficient solution for a class of nonconvex and nonsmooth vector optimization problems in Banach spaces. We show the equivalence between the nonconvex and nonsmooth vector optimization problem and the vector variationallike inequality involving setvalued mappings. We prove ..."
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Cited by 1 (0 self)
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We consider the weakly efficient solution for a class of nonconvex and nonsmooth vector optimization problems in Banach spaces. We show the equivalence between the nonconvex and nonsmooth vector optimization problem and the vector variationallike inequality involving setvalued mappings. We prove some existence results concerned with the weakly efficient solution for the nonconvex and nonsmooth vector optimization problems by using the equivalence and FanKKM theorem under some suitable conditions.
SOLUTIONS FOR NONLINEAR VARIATIONAL INEQUALITIES WITH A NONSMOOTH POTENTIAL
, 2003
"... First we examine a resonant variational inequality driven by the pLaplacian and with a nonsmooth potential. We prove the existence of a nontrivial solution. Then we use this existence theorem to obtain nontrivial positive solutions for a class of resonant elliptic equations involving the pLaplaci ..."
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First we examine a resonant variational inequality driven by the pLaplacian and with a nonsmooth potential. We prove the existence of a nontrivial solution. Then we use this existence theorem to obtain nontrivial positive solutions for a class of resonant elliptic equations involving the pLaplacian and a nonsmooth potential. Our approach is variational based on the nonsmooth critical point theory for functionals of the form ϕ = ϕ1 +ϕ2 with ϕ1 locally Lipschitz and ϕ2 proper, convex, lower semicontinuous. 1.