In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery p...In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.展开更多
A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided proje...A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm.展开更多
In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatu...In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatures have demonstrated that our algorithm is effective.展开更多
In this paper, a smoothing QP-free infeasible method is proposed for nonlinear inequality constrained optimization problems. This iterative method is based on the solution of nonlinear equations which is obtained by t...In this paper, a smoothing QP-free infeasible method is proposed for nonlinear inequality constrained optimization problems. This iterative method is based on the solution of nonlinear equations which is obtained by the multipliers and the smoothing FisheroBurmeister function for the KKT first-order optimality conditions. Comparing with other QP-free methods, this method does not request the strict feasibility of iteration. In particular, this method is implementable and globally convergent without assuming the strict complementarity condition and the isolatedness of accumulation points. ~rthermore, the gradients of active constraints are not requested to be linearly independent. Preliminary numerical results indicate that this smoothing QP-free infeasible method is quite promising.展开更多
In this paper, we are concerned with properties of positive solutions of the following Euler-Lagrange system associated with the weighted Hardy-Littlewood-Sobolev inequality in discrete form{uj =∑ k ∈Zn vk^q/(1 + ...In this paper, we are concerned with properties of positive solutions of the following Euler-Lagrange system associated with the weighted Hardy-Littlewood-Sobolev inequality in discrete form{uj =∑ k ∈Zn vk^q/(1 + |j|)^α(1 + |k- j|)^λ(1 + |k|)^β,(0.1)vj =∑ k ∈Zn uk^p/(1 + |j|)^β(1 + |k- j|)^λ(1 + |k|)^α,where u, v 〉 0, 1 〈 p, q 〈 ∞, 0 〈 λ 〈 n, 0 ≤α + β≤ n- λ,1/p+1〈λ+α/n and 1/p+1+1/q+1≤λ+α+β/n:=λ^-/n. We first show that positive solutions of(0.1) have the optimal summation interval under assumptions that u ∈ l^p+1(Z^n) and v ∈ l^q+1(Z^n). Then we show that problem(0.1) has no positive solution if 0 〈λˉ pq ≤ 1 or pq 〉 1 and max{(n-λ^-)(q+1)/pq-1,(n-λ^-)(p+1)/pq-1} ≥λ^-.展开更多
This paper studies the limit average variance criterion for continuous-time Markov decision processes in Polish spaces. Based on two approaches, this paper proves not only the existence of solutions to the variance mi...This paper studies the limit average variance criterion for continuous-time Markov decision processes in Polish spaces. Based on two approaches, this paper proves not only the existence of solutions to the variance minimization optimality equation and the existence of a variance minimal policy that is canonical, but also the existence of solutions to the two variance minimization optimality inequalities and the existence of a variance minimal policy which may not be canonical. An example is given to illustrate all of our conditions.展开更多
In this paper, an improved feasible QP-free method is proposed to solve nonlinear inequality constrained optimization problems. Here, a new modified method is presented to obtain the revised feasible descent direction...In this paper, an improved feasible QP-free method is proposed to solve nonlinear inequality constrained optimization problems. Here, a new modified method is presented to obtain the revised feasible descent direction. In view of the computational cost, the most attractive feature of the new algorithm is that only one system of linear equations is required to obtain the revised feasible descent direction. Thereby, per single iteration, it is only necessary to solve three systems of linear equations with the same coefficient matrix. In particular, without the positive definiteness assumption on the Hessian estimate, the proposed algorithm is still global convergence. Under some suitable conditions, the superlinear convergence rate is obtained.展开更多
This paper presents a new trust-region algorithm for n-dimension nonlinear optimization subject to m nonlinear inequality constraints. Equivalent KKT conditions are derived, which is the basis for constructing the new...This paper presents a new trust-region algorithm for n-dimension nonlinear optimization subject to m nonlinear inequality constraints. Equivalent KKT conditions are derived, which is the basis for constructing the new algorithm. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps, local quadratic convergence theorem is proved for nondegenerate minimizer point. Numerical experiment is presented to show the effectiveness of our approach.展开更多
In this paper we study the average sample-path cost (ASPC) problem for continuous-time Markov decision processes in Polish spaces. To the best of our knowledge, this paper is a first attempt to study the ASPC criter...In this paper we study the average sample-path cost (ASPC) problem for continuous-time Markov decision processes in Polish spaces. To the best of our knowledge, this paper is a first attempt to study the ASPC criterion on continuous-time MDPs with Polish state and action spaces. The corresponding transition rates are allowed to be unbounded, and the cost rates may have neither upper nor lower bounds. Under some mild hypotheses, we prove the existence of (ε〉 0)-ASPC optimal stationary policies based on two different approaches: one is the "optimality equation" approach and the other is the "two optimality inequalities" approach.展开更多
We consider a mathematical model which describes a contact between a deformable body and a foundation. The contact is bilateral and modelled with Tresca's friction law. The goal of this paper is to study an optimal c...We consider a mathematical model which describes a contact between a deformable body and a foundation. The contact is bilateral and modelled with Tresca's friction law. The goal of this paper is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target, by acting with a control on the boundary of the body. We state an optimal control problem which admits at least one solution. We also introduce the regularized control problem for which we study the convergence when the regularization parameter tends to zero. Finally, an optimally condition is established for this problem.展开更多
This paper presents a strong subfeasible directions algorithm possessing superlinear convergence for inequality constrained optimization. The starting point of this algorithm may be arbitary and its feasibility is mon...This paper presents a strong subfeasible directions algorithm possessing superlinear convergence for inequality constrained optimization. The starting point of this algorithm may be arbitary and its feasibility is monotonically increasing. The search directions only depend on solving one quadratic proraming and its simple correction, its line search is simple straight search and does not depend on any penalty function. Under suit assumptions, the algorithm is proved to possess global and superlinear convergence.展开更多
基金Supported by the National Fund of Natural Sciences.
文摘In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.
文摘A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm.
文摘In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatures have demonstrated that our algorithm is effective.
基金Supported-by the National Natural Science Foundation of China(10371089)and the Foundation of Qingdao University
文摘In this paper, a smoothing QP-free infeasible method is proposed for nonlinear inequality constrained optimization problems. This iterative method is based on the solution of nonlinear equations which is obtained by the multipliers and the smoothing FisheroBurmeister function for the KKT first-order optimality conditions. Comparing with other QP-free methods, this method does not request the strict feasibility of iteration. In particular, this method is implementable and globally convergent without assuming the strict complementarity condition and the isolatedness of accumulation points. ~rthermore, the gradients of active constraints are not requested to be linearly independent. Preliminary numerical results indicate that this smoothing QP-free infeasible method is quite promising.
基金supported by NNSF of China(11261023,11326092),NNSF of China(11271170)Startup Foundation for Doctors of Jiangxi Normal University+1 种基金GAN PO 555 Program of JiangxiNNSF of Jiangxi(20122BAB201008)
文摘In this paper, we are concerned with properties of positive solutions of the following Euler-Lagrange system associated with the weighted Hardy-Littlewood-Sobolev inequality in discrete form{uj =∑ k ∈Zn vk^q/(1 + |j|)^α(1 + |k- j|)^λ(1 + |k|)^β,(0.1)vj =∑ k ∈Zn uk^p/(1 + |j|)^β(1 + |k- j|)^λ(1 + |k|)^α,where u, v 〉 0, 1 〈 p, q 〈 ∞, 0 〈 λ 〈 n, 0 ≤α + β≤ n- λ,1/p+1〈λ+α/n and 1/p+1+1/q+1≤λ+α+β/n:=λ^-/n. We first show that positive solutions of(0.1) have the optimal summation interval under assumptions that u ∈ l^p+1(Z^n) and v ∈ l^q+1(Z^n). Then we show that problem(0.1) has no positive solution if 0 〈λˉ pq ≤ 1 or pq 〉 1 and max{(n-λ^-)(q+1)/pq-1,(n-λ^-)(p+1)/pq-1} ≥λ^-.
基金supported by the National Natural Science Foundation of China(10801056)the Natural Science Foundation of Ningbo(2010A610094)
文摘This paper studies the limit average variance criterion for continuous-time Markov decision processes in Polish spaces. Based on two approaches, this paper proves not only the existence of solutions to the variance minimization optimality equation and the existence of a variance minimal policy that is canonical, but also the existence of solutions to the two variance minimization optimality inequalities and the existence of a variance minimal policy which may not be canonical. An example is given to illustrate all of our conditions.
基金Supported by National Natural Science Foundation of China (Grant Nos. 11061011 and 71061002)Guangxi Fund for Distinguished Young Scholars (2012GXSFFA060003)
文摘In this paper, an improved feasible QP-free method is proposed to solve nonlinear inequality constrained optimization problems. Here, a new modified method is presented to obtain the revised feasible descent direction. In view of the computational cost, the most attractive feature of the new algorithm is that only one system of linear equations is required to obtain the revised feasible descent direction. Thereby, per single iteration, it is only necessary to solve three systems of linear equations with the same coefficient matrix. In particular, without the positive definiteness assumption on the Hessian estimate, the proposed algorithm is still global convergence. Under some suitable conditions, the superlinear convergence rate is obtained.
基金the Scientific Research Foundation of Hunan Provincial Education Department, No. 02B021, and the National Natural Science Foundation of China, No. 10171008.
文摘This paper presents a new trust-region algorithm for n-dimension nonlinear optimization subject to m nonlinear inequality constraints. Equivalent KKT conditions are derived, which is the basis for constructing the new algorithm. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps, local quadratic convergence theorem is proved for nondegenerate minimizer point. Numerical experiment is presented to show the effectiveness of our approach.
基金Supported by the National Natural Science Foundation of China (No.10801056)the Natural Science Foundation of Ningbo (No. 2010A610094)K.C. Wong Magna Fund in Ningbo University
文摘In this paper we study the average sample-path cost (ASPC) problem for continuous-time Markov decision processes in Polish spaces. To the best of our knowledge, this paper is a first attempt to study the ASPC criterion on continuous-time MDPs with Polish state and action spaces. The corresponding transition rates are allowed to be unbounded, and the cost rates may have neither upper nor lower bounds. Under some mild hypotheses, we prove the existence of (ε〉 0)-ASPC optimal stationary policies based on two different approaches: one is the "optimality equation" approach and the other is the "two optimality inequalities" approach.
文摘We consider a mathematical model which describes a contact between a deformable body and a foundation. The contact is bilateral and modelled with Tresca's friction law. The goal of this paper is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target, by acting with a control on the boundary of the body. We state an optimal control problem which admits at least one solution. We also introduce the regularized control problem for which we study the convergence when the regularization parameter tends to zero. Finally, an optimally condition is established for this problem.
基金Supported by the National Natural Sciences Foundation of China (No.39830070 and 10171055).
文摘In this paper, a new SQP method for inequality constrained optimization is proposed and the global convergence is obtained under very mild conditions.
文摘This paper presents a strong subfeasible directions algorithm possessing superlinear convergence for inequality constrained optimization. The starting point of this algorithm may be arbitary and its feasibility is monotonically increasing. The search directions only depend on solving one quadratic proraming and its simple correction, its line search is simple straight search and does not depend on any penalty function. Under suit assumptions, the algorithm is proved to possess global and superlinear convergence.