The Experts below are selected from a list of 20259 Experts worldwide ranked by ideXlab platform
Mihai Postolache - One of the best experts on this subject based on the ideXlab platform.
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forward backward splitting algorithm for fixed point problems and zeros of the sum of monotone operators
Arabian Journal of Mathematics, 2020Co-Authors: Vahid Dadashi, Mihai PostolacheAbstract:In this paper, we construct a forward–backward splitting algorithm for approximating a zero of the sum of an $$\alpha $$-inverse strongly monotone operator and a maximal monotone operator. The strong convergence theorem is then proved under mild conditions. Then, we add a nonexpansive mapping in the algorithm and prove that the generated Sequence Converges strongly to a common element of a fixed points set of a nonexpansive mapping and zero points set of the sum of monotone operators. We apply our main result both to equilibrium problems and convex programming.
Wen-jun Cao - One of the best experts on this subject based on the ideXlab platform.
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On functional approximation of the equivalent control using learning variable structure control
IEEE Transactions on Automatic Control, 2002Co-Authors: Wen-jun CaoAbstract:A learning variable structure control (LVSC) approach is originated to obtain the equivalent control of a general class of multiple-input-multiple-output (MIMO) variable structure systems under repeatable control tasks. LVSC synthesizes variable structure control (VSC) as the robust part which stabilizes the system, and learning control (LC) as the "plug-in" intelligent part which completely nullifies the effects of the matched uncertainties on tracking error. Rigorous proof based on energy function and functional analysis shows. that the tracking error Sequence Converges uniformly to zero, and that the bounded LC Sequence Converges to the equivalent control almost everywhere.
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A Learning Variable Structure Controller of a Flexible One-Link Manipulator
Journal of Dynamic Systems Measurement and Control, 2000Co-Authors: Wen-jun CaoAbstract:In this paper, tip regulation of a flexible one-link manipulator by Learning Variable Structure Control (LVSC) is investigated. Switching surface is designed according to a selected reference model which relocates system poles to be negative real ones, hence link vibration is eliminated. The proposed LVSC incorporates a learning mechanism to improve regulation accuracy. Rigorous proof shows: the tracking error Sequence Converges uniformly to zero; the uniformly bounded learning control Sequence Converges to the equivalent control almost everywhere. For practical considerations, the learning mechanism is further conducted in frequency domain by means of Fourier series expansion, hence achieves better regulation performance. Numerical simulations confirm the effectiveness and robustness of the proposed approach. [S0022-0434(00)01804-9]
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A learning variable structure controller of a flexible one-link manipulator
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 1Co-Authors: Wen-jun CaoAbstract:Tip regulation of a flexible one-link manipulator by learning variable structure control (LVSC) is investigated. The sliding surface is designed according to a selected reference model which relocates system poles to be negative real ones, hence link vibration is eliminated. The proposed LVSC incorporates a learning mechanism to improve regulation accuracy. Rigorous proof shows: the state's tracking error Sequence Converges uniformly to zero; the uniformly bounded learning control Sequence Converges to the equivalent control almost everywhere.
Poom Kumam - One of the best experts on this subject based on the ideXlab platform.
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a new hybrid iterative method for solution of equilibrium problems and fixed point problems for an inverse strongly monotone operator and a nonexpansive mapping
Journal of Applied Mathematics and Computing, 2009Co-Authors: Poom KumamAbstract:In this paper, we introduce an iterative scheme by a new hybrid method for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in a real Hilbert space. We show that the iterative Sequence Converges strongly to a common element of the above three sets under some parametric controlling conditions by the new hybrid method which is introduced by Takahashi et al. (J. Math. Anal. Appl., doi: 10.1016/j.jmaa.2007.09.062, 2007). The results are connected with Tada and Takahashi’s result [A. Tada and W. Takahashi, Weak and strong convergence theorems for a nonexpansive mappings and an equilibrium problem, J. Optim. Theory Appl. 133, 359–370, 2007]. Moreover, our result is applicable to a wide class of mappings.
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weak convergence theorem by an extragradient method for variational inequality equilibrium and fixed point problems
2009Co-Authors: Malaysian Mathematical, Poom Kumam, Chaichana Jaiboon, Usa HumphriesAbstract:In this paper, we introduce a new iterative scheme for finding the common element of the set of: fixed points; equilibrium; and the variational inequality problems for monotone and k-Lipschitz continuous mappings. The iterative process is based on the so-called extragradient method. We show that the Sequence Converges weakly to a common element of the above three sets under some parameter controlling conditions. This main theorem extends a recent result of Nadezhkiha and Takahashi (7).
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a hybrid approximation method for equilibrium and fixed point problems for a monotone mapping and a nonexpansive mapping
Nonlinear Analysis: Hybrid Systems, 2008Co-Authors: Poom KumamAbstract:The purpose of this paper is to present an iterative scheme by a hybrid method for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in the framework of a Hilbert space. We show that the iterative Sequence Converges strongly to a common element of the above three sets under appropriate conditions. Additionally, the idea of our results are applied to find a zero of a maximal monotone operator and a strictly pseudocontractive mapping in a real Hilbert space.
Uday V. Shanbhag - One of the best experts on this subject based on the ideXlab platform.
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On Stochastic Mirror-prox Algorithms for Stochastic Cartesian Variational Inequalities: Randomized Block Coordinate and Optimal Averaging Schemes
Set-valued and Variational Analysis, 2018Co-Authors: Farzad Yousefian, Angelia Nedic, Uday V. ShanbhagAbstract:Motivated by multi-user optimization problems and non-cooperative Nash games in uncertain regimes, we consider stochastic Cartesian variational inequality problems where the set is given as the Cartesian product of a collection of component sets. First, we consider the case where the number of the component sets is large and develop a randomized block stochastic mirror-prox algorithm, where at each iteration only a randomly selected block coordinate of the solution vector is updated through implementing two consecutive projection steps. We show that when the mapping is strictly pseudo-monotone, the algorithm generates a Sequence of iterates that Converges to the solution of the problem almost surely. When the maps are strongly pseudo-monotone, we prove that the mean-squared error diminishes at the optimal rate. Second, we consider large-scale stochastic optimization problems with convex objectives and develop a new averaging scheme for the randomized block stochastic mirror-prox algorithm. We show that by using a different set of weights than those employed in the classical stochastic mirror-prox methods, the objective values of the averaged Sequence Converges to the optimal value in the mean sense at an optimal rate. Third, we consider stochastic Cartesian variational inequality problems and develop a stochastic mirror-prox algorithm that employs the new weighted averaging scheme. We show that the expected value of a suitably defined gap function Converges to zero at an optimal rate.
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On stochastic mirror-prox algorithms for stochastic Cartesian variational inequalities: randomized block coordinate, and optimal averaging schemes
arXiv: Optimization and Control, 2016Co-Authors: Farzad Yousefian, Angelia Nedich, Uday V. ShanbhagAbstract:Motivated by multi-user optimization problems and non-cooperative Nash games in uncertain regimes, we consider stochastic Cartesian variational inequalities (SCVI) where the set is given as the Cartesian product of a collection of component sets. First, we consider the case where the number of the component sets is large. For solving this type of problems, the classical stochastic approximation methods and their prox generalizations are computationally inefficient as each iteration becomes very costly. To address this challenge, we develop a randomized block stochastic mirror-prox (B-SMP) algorithm, where at each iteration only a randomly selected block coordinate of the solution is updated through implementing two consecutive projection steps. Under standard assumptions on the problem and settings of the algorithm, we show that when the mapping is strictly pseudo-monotone, the algorithm generates a Sequence of iterates that Converges to the solution of the problem almost surely. To derive rate statements, we assume that the maps are strongly pseudo-monotone and obtain {a non-asymptotic mean squared error $\mathcal{O}\left(\frac{d}{k}\right)$, where $k$ is the iteration number and $d$ is the number of component sets. Second, we consider large-scale stochastic optimization problems with convex objectives. For this class of problems, we develop a new averaging scheme for the B-SMP algorithm. Unlike the classical averaging stochastic mirror-prox (SMP) method where a decreasing set of weights for the averaging Sequence is used, here we consider a different set of weights that are characterized in terms of the stepsizes and a {parameter}. We show that using such weights, the objective values of the averaged Sequence Converges to the optimal value in the mean sense with the rate $\mathcal{O}\left(\frac{\sqrt{d}}{\sqrt{k}}\right)$.
Xiangsun Zhang - One of the best experts on this subject based on the ideXlab platform.
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A smoothing Levenberg–Marquardt method for NCP
Applied Mathematics and Computation, 2006Co-Authors: Ju-liang Zhang, Xiangsun ZhangAbstract:Abstract In this paper, we convert the nonlinear complementarity problems to an equivalent smooth nonlinear equation system by using smoothing technique. Then we use Levenberg–Marquardt type method to solve the nonlinear equation system. The method has the following merits: (i) any cluster point of the iteration Sequence is a solution of the P 0 − NCP; (ii) it generates a bounded Sequence if the P 0 − NCP has a nonempty and bounded solution set; (iii) if the generalized Jacobian is nonsingular at a solution point, then the whole Sequence Converges to the (unique) solution of the P 0 − NCP superlinearly; (iv) for the P 0 − NCP, if an accumulation point of the iteration Sequence satisfies strict complementary condition, then the whole Sequence Converges to this accumulation point superlinearly.
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A smoothing Levenberg-Marquardt method for NCP q
2006Co-Authors: Ju-liang Zhang, Xiangsun ZhangAbstract:In this paper, we convert the nonlinear complementarity problems to an equivalent smooth nonlinear equation system by using smoothing technique. Then we use Levenberg–Marquardt type method to solve the nonlinear equation system. The method has the following merits: (i) any cluster point of the iteration Sequence is a solution of the P0 � NCP; (ii) it generates a bounded Sequence if the P0 � NCP has a nonempty and bounded solution set; (iii) if the generalized Jacobian is nonsingular at a solution point, then the whole Sequence Converges to the (unique) solution of the P0 � NCP superlinearly; (iv) for the P0 � NCP, if an accumulation point of the iteration Sequence satisfies strict complementary condition, then the whole Sequence Converges to this accumulation point superlinearly.
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A smoothing Levenberg-Marquardt method for NCP
Applied Mathematics and Computation, 2006Co-Authors: Ju-liang Zhang, Xiangsun ZhangAbstract:Abstract In this paper, we convert the nonlinear complementarity problems to an equivalent smooth nonlinear equation system by using smoothing technique. Then we use Levenberg–Marquardt type method to solve the nonlinear equation system. The method has the following merits: (i) any cluster point of the iteration Sequence is a solution of the P 0 − NCP; (ii) it generates a bounded Sequence if the P 0 − NCP has a nonempty and bounded solution set; (iii) if the generalized Jacobian is nonsingular at a solution point, then the whole Sequence Converges to the (unique) solution of the P 0 − NCP superlinearly; (iv) for the P 0 − NCP, if an accumulation point of the iteration Sequence satisfies strict complementary condition, then the whole Sequence Converges to this accumulation point superlinearly.
