This paper is concerned with the H-infinity filtering problem for polynomial systems. By means of Lyapunov theory and matrix inequality techniques, sufficient conditions are first obtained to ensure that the filtering...
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This paper is concerned with the H-infinity filtering problem for polynomial systems. By means of Lyapunov theory and matrix inequality techniques, sufficient conditions are first obtained to ensure that the filtering error system is asymptotically stable and satisfies H-infinity performance constraint. Then, a sufficient condition for the existence of desired filters is established with a free matrix introduced, which will greatly facilitate the design of filter matrices. By virtue of sum-of-squares (SOS) approaches, a convergent iterative algorithm is developed to tackle the polynomial H-infinity filtering problem. Note that the approach can be efficiently implemented by means of recently developed SOS decomposition techniques, and the filter matrices can be designed explicitly. Finally, a numerical example is given to illustrate the main results of this paper. (C) 2011 Elsevier B.V. All rights reserved.
In this paper, we introduce and study a new class of variational inclusions in Banach spaces. As it concerns the methods of solution, we introduce a new class of monotone mappings. We define a proximal mapping associa...
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In this paper, we introduce and study a new class of variational inclusions in Banach spaces. As it concerns the methods of solution, we introduce a new class of monotone mappings. We define a proximal mapping associated with this mappings and show its Lipschitz continuity. By using the technique of proximal mapping, we construct a new iterative algorithm. Under some suitable conditions, we prove the convergence of iterative sequences generated by the algorithm. Our results improve and generalize many known results.
A system of generalized mixed equilibrium-like problems is introduced and the existence of its solutions is shown by using the auxiliary principle technique in Hilbert spaces.
A system of generalized mixed equilibrium-like problems is introduced and the existence of its solutions is shown by using the auxiliary principle technique in Hilbert spaces.
Evaluating or predicting the quality of protein models (i.e., predicted protein tertiary structures) without knowing their native structures is important for selecting and appropriately using protein models. We descri...
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Evaluating or predicting the quality of protein models (i.e., predicted protein tertiary structures) without knowing their native structures is important for selecting and appropriately using protein models. We describe an iterative approach that improves the performances of protein Model Quality Assurance Programs (MQAPs). Given the initial quality scores of a list of models assigned by a MQAP, the method iteratively refines the scores until the ranking of the models does not change. We applied the method to the model quality assessment data generated by 30 MQAPs during the Eighth Critical Assessment of Techniques for Protein Structure Prediction. To various degrees, our method increased the average correlation between predicted and real quality scores of 25 out of 30 MQAPs and reduced the average loss (i.e., the difference between the top ranked model and the best model) for 28 MQAPs. Particularly, for MQAPs with low average correlations (<0.4), the correlation can be increased by several times. Similar experiments conducted on the CASP9 MQAPs also demonstrated the effectiveness of the method. Our method is a hybrid method that combines the original method of a MQAP and the pair-wise comparison clustering method. It can achieve a high accuracy similar to a full pair-wise clustering method, but with much less computation time when evaluating hundreds of models. Furthermore, without knowing native structures, the iterative refining method can evaluate the performance of a MQAP by analyzing its model quality predictions.
The purpose of this paper is to introduce a split equilibrium problem (SEP) and find a solution of the equilibrium problem such that its image under a given bounded linear operator is a solution of another equilibrium...
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The purpose of this paper is to introduce a split equilibrium problem (SEP) and find a solution of the equilibrium problem such that its image under a given bounded linear operator is a solution of another equilibrium problem. By using the iterative method, we construct some iterative algorithms to solve such problem in real Hilbert spaces and obtain some strong and weak convergence theorems. Finally, we point out that there exist many SEPs which need the use of new methods to solve them. Some examples are given to illustrate our results.
Extensive research in recent years has shown that dynamic spectrum sharing is a promising ap- proach to＇address the artificial spectrum scarcity problem by improving spectrum utilization. This new communication parad...
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Extensive research in recent years has shown that dynamic spectrum sharing is a promising ap- proach to＇address the artificial spectrum scarcity problem by improving spectrum utilization. This new communication paradigm, however, requires a well-designed spectrum allocation mechanism. This paper designs a double spectrum auction framework that allows unlicensed secondary users to obtain selected idle spectra assigned to licensed primary users. This is a win-win game because primary users can earn extra revenue and secondary users can obtain spectra they desperately need. The competition among primary users in the auction framework is studied combining game theory with a double spectrum auction in a non-cooperative game with the Nash Equilibrium （NE） as the best solution. Primary users use the prices obtained from the NE as their bid strategies to participate in the auction. In this auction sellers and buyers bid privately and confidentially, which means that the secondary users do not actually know the price and the spectrum size offered by the primary users, then a new net utility function was developed for the primary users with an iterative algorithm to find the Nash equilibrium point. Simulations demonstrate that this design effectively improves spectrum utilization.
We present an iterative sampling method which delivers upper and lower bounding processes for the Brownian path. We develop such processes with particular emphasis on being able to unbiasedly simulate them on a person...
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We present an iterative sampling method which delivers upper and lower bounding processes for the Brownian path. We develop such processes with particular emphasis on being able to unbiasedly simulate them on a personal computer. The dominating processes converge almost surely in the supremum and L-1 norms. In particular, the rate of converge in L-1 is of the order O(K-1/2), K denoting the computing cost. The as. enfolding of the Brownian path can be exploited in Monte Carlo applications involving Brownian paths whence our algorithm (termed the epsilon-strong algorithm) can deliver unbiased Monte Carlo estimators over path expectations, overcoming discretisation errors characterising standard approaches. We will show analytical results from applications of the epsilon-strong algorithm for estimating expectations arising in option pricing. We will also illustrate that individual steps of the algorithm can be of separate interest, giving new simulation methods for interesting Brownian distributions.
We introduce implicit and explicit iterative algorithms for the construction of fixed points of pseudocontractions T in Hilbert spaces. We prove that the proposed iterative algorithms converge strongly to the minimum-...
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We introduce implicit and explicit iterative algorithms for the construction of fixed points of pseudocontractions T in Hilbert spaces. We prove that the proposed iterative algorithms converge strongly to the minimum-norm fixed point of T. Moreover we show that some of the existing iterative algorithms for nonexpansive mappings fail to converge when applied to pseudocontractions.
Finding iterative algorithms to approximate fixed points for nonexpansive mappings is a very, active topic in a number of mathematical and engineering areas, in particular, in image recovery and signal processing. Con...
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ISBN:
(纸本)9781424420957
Finding iterative algorithms to approximate fixed points for nonexpansive mappings is a very, active topic in a number of mathematical and engineering areas, in particular, in image recovery and signal processing. Considerable research efforts have been devoted to the study of this area in recent years. By now, there already exist some algorithms, but they are not quite enough to deal with problems of finding common fixed points of infinite nonexpansive mappings. In this paper, a more general form of iterative algorithm is introduced which is proved to be strongly convergent to common fixed point of infinite nonexpansive mappings in a real strictly convex and uniformly smooth Banach space by using sonic new techniques.
In this paper, we study a new system of generalized mixed equilibrium problems involving nonmonotone set-valued mappings and nondifferential bifunctions in Banach spaces. First, a system of auxiliary generalized mixed...
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In this paper, we study a new system of generalized mixed equilibrium problems involving nonmonotone set-valued mappings and nondifferential bifunctions in Banach spaces. First, a system of auxiliary generalized mixed equilibrium problems are introduced. By using a minimax inequality, the existence and uniqueness of solutions of the system of auxiliary generalized mixed equilibrium problems is proved. Next, by using the auxiliary principle technique, an iterative algorithm for solving the system of generalized mixed equilibrium problems is constructed. Finally, the existence of solutions and the convergence of iterative sequences generated by the algorithm are proved under suitable conditions. These results improve, unify, and generalize many corresponding known results given in literature.
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