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Home > Papers > Optimization

There are 49 papers published in subject: > since this site started.

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	1. Remarks on Regularized Gap Functions and Error Bounds for Vector Variational Inequalities
	Li Lili,Chen Chunrong
	Mathematics 04 November 2013
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	Abstract:In this paper, modified versions of corresponding results on error bounds for (generalized) vector variational inequalities obtained by Sun and Chai (Optim. Lett., 2013) are given. Moreover, a framework to construct regularized gap functions for (generalized) vector variational inequalities is established. The main results obtained are new in the literature.
	TO cite this article:Li Lili,Chen Chunrong. Remarks on Regularized Gap Functions and Error Bounds for Vector Variational Inequalities[OL].[ 4 November 2013] http://en.paper.edu.cn/en_releasepaper/content/4567993


	2. A LEGENDRE-GALERKIN SPECTRAL METHOD FOR FLOW OPTIMALCONTROL PROBLEM WITH $H^1$-NORM STATE CONSTRAINT
	CHEN Yan-Ping, HUANG Feng-Lin
	Mathematics 04 October 2013
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	Abstract:In this paper, we consider an optimal control problem with $H^1$-normsate constraint, governed by Stokes equations.The control problem is approximated by Legendre-Galerkin spectral method,which provides very accurate approximations with a relatively small number ofunknowns. Choosing appropriate basis functions leads to discrete systemswith sparse matrices. We first proposed the optimality conditions ofthe exact and the discrete optimal control systems, thenderive both a priori and a posteriori error estimates for controlproblem. Finally, an illustrative numerical experiment indicate that the proposed method is veryeffective for this kind of control problems.
	TO cite this article:CHEN Yan-Ping, HUANG Feng-Lin. A LEGENDRE-GALERKIN SPECTRAL METHOD FOR FLOW OPTIMALCONTROL PROBLEM WITH $H^1$-NORM STATE CONSTRAINT[OL].[ 4 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4561453

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	3. A Nonmonotonic Self-Adaptive Trust Region Algorithm Without Line Search
	Hang Dan,Zhou Qunyan
	Mathematics 01 October 2013
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	Abstract:In this paper,we propose a nonmonotone trust region method for unconstrained optimization.Our method can be regarded as a combination of nonmonotone technique ,fixed steplength and self-adaptive trust region,when a trial step is not accepted ,the method doesn't resolve the subproblem but generates a iterative point whose steplength is defined by formula. Under mild conditions,we prove that the algorithm is global convergence and superlinear convergence. Numerical results are also presented.
	TO cite this article:Hang Dan,Zhou Qunyan. A Nonmonotonic Self-Adaptive Trust Region Algorithm Without Line Search[OL].[ 1 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4562233


	4. On Holder Continuity of Solutions to Parametric Vector Quasiequilibrium Problems
	CHEN Chun-Rong
	Mathematics 25 September 2013
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	Abstract:In this paper, Holder continuity of the unique solution to a parametric vector quasiequilibrium problem is studied by using nonlinear scalarization approach. The well-known Gerstewitz nonlinear scalarization function as an efficient tool plays key roles, especially, its globally Lipschitz property is fully employed. The result obtained is new in the literature, and the approach via nonlinear scalarization is different from the ones used in related works.
	TO cite this article:CHEN Chun-Rong. On Holder Continuity of Solutions to Parametric Vector Quasiequilibrium Problems[OL].[25 September 2013] http://en.paper.edu.cn/en_releasepaper/content/4561643


	5. A Proximal Method for Solving Vector Variational Inequalities
	CHEN Chun-Rong
	Mathematics 25 September 2013
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	Abstract:In this paper, based on choosing at each iteration a different vectorization to the iterated matrix, a proximal-type method for solving the weak vector variational inequality problem (mbox{WVVI}) in finite-dimensional spaces is proposed. Under appropriate assumptions, it was proved that the generated subsequence converges to a solution of problem $(mbox{WVVI})$, if the problem $(mbox{WVVI})$ has strong solutions. Moreover, if the solution set of $(mbox{WVVI})$ coincides with its strong solution set, then the whole sequence converges to a strong solution of problem (mbox{WVVI}).
	TO cite this article:CHEN Chun-Rong. A Proximal Method for Solving Vector Variational Inequalities[OL].[25 September 2013] http://en.paper.edu.cn/en_releasepaper/content/4561636


	6. An Aggregate Function Method for Constrained Optimization Problems
	ZHANG Xinchun
	Mathematics 30 June 2013
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	Abstract:In this paper, the aggregate function method (AFM) for constrained optimization problems (COP) is investigated. The AFM is effective for multiple inequality-constrained optimization problems. However, the inherent shortcomings of the AFM, both in convergence and data overflow, seem to have gone unnoticed. To address these issues systematically, some efficient measurements are carried out to deal with such problems, such as adding the stable term and the exponent reduction parameter to the original aggregate function, which are highlighted in the entire paper. Moreover, the corresponding properties of both the AFM and the improved AFM (IAFM) are presented.
	TO cite this article:ZHANG Xinchun. An Aggregate Function Method for Constrained Optimization Problems[J].


	7. An accelerated first-order gradient algorithm for singly linearly constrained quadratic programs with box constraints
	Li Mingqiang,Han Congying ,Wang Yongli,He Guoping
	Mathematics 20 January 2013
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	Abstract:In this paper, we propose an accelerated proximal gradient algorithm for singly linearly constrained quadratic programs with box constraints.At each iteration, the subproblem whose Hessian matrix is diagonal and positive definite is an easy model which can be solved efficiently via searching a root of a piecewise linear function. It is proved that the new algorithm can terminate at an $arepsilon-$optimal solution within $O(1/sqrt arepsilon)$ iterations. Moreover, no line search is needed in this new algorithm and the global convergence can be proved under mild conditions. Numerical results arereported for solving quadratic programs arising from the training of support vector machines, which show that the new algorithm is efficient.
	TO cite this article:Li Mingqiang,Han Congying ,Wang Yongli, et al. An accelerated first-order gradient algorithm for singly linearly constrained quadratic programs with box constraints[OL].[20 January 2013] http://en.paper.edu.cn/en_releasepaper/content/4516737


	8. The Existence of Optimal Control for Fully Coupled Forward-Backward Stochastic Differential Equation System with Non-Lipschitz Cost Functional
	MENG Qingxin,ZHANG Qi
	Mathematics 18 December 2012
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	Abstract:In this paper, we study the existence of stochastic optimal control by a new application of the existence theorem of convex optimality. The stochastic system in our concern is a linear fully coupled forward-backward stochastic differential equation with a non-Lipschitz cost functional. Some typical examples, such as LQ problem, can be included in this studied stochastic system.
	TO cite this article:MENG Qingxin,ZHANG Qi. The Existence of Optimal Control for Fully Coupled Forward-Backward Stochastic Differential Equation System with Non-Lipschitz Cost Functional[OL].[18 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4504577


	9. A line search filter-SQP method for nonlinear inequality constrained optimization
	YUAN Jing,ZHU Detong
	Mathematics 19 June 2012
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	Abstract:Filter methods are extensively studied for solving nonlinearprogramming problems (NLP). In this paper, the author propose the sequencequadratic programming method with a line search filter technique fornonlinear inequality constrained problems. The search direction ofthis algorithm is generated by first-order necessary conditions,while a backtracking line search procedure is used to generate stepsize. The second order correction is employed to overcome theMaratos effect. Local convergent rate and global convergence areestablished under some suitable conditions. Finally, the results ofnumerical experiments indicate that the proposed method is efficientfor the given test problems.
	TO cite this article:YUAN Jing,ZHU Detong. A line search filter-SQP method for nonlinear inequality constrained optimization[OL].[19 June 2012] http://en.paper.edu.cn/en_releasepaper/content/4482733


	10. A Conjugate Gradient Path Method without Line Search Technique for Unconstrained Optimization
	WANG Jueyu,ZHU Detong
	Mathematics 18 April 2012
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	Abstract:In this paper, we propose a new approach via discrete conjugate gradient path for solving unconstrained optimization. The conjugate gradient path is obtained by constructing quadratic model of the objective function. The global convergence and local quadratic or superlinear convergence rate of the proposed algorithm are established under some reasonable conditions. Finally, the numerical results are reported to show the effectiveness of the proposed algorithm.
	TO cite this article:WANG Jueyu,ZHU Detong. A Conjugate Gradient Path Method without Line Search Technique for Unconstrained Optimization[OL].[18 April 2012] http://en.paper.edu.cn/en_releasepaper/content/4474920

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