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W0^1p(x) Versus C^1 Local Minimizers for a Functional with Critical Growth
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作者 SAOUDI K 《Journal of Partial Differential Equations》 2014年第2期115-124,共10页
Let Ω IR^N, (N ≥ 2) be a bounded smooth domain, p is Holder continuous on Ω^-, 1 〈 p^- := inf pΩ(x) ≤ p+ = supp(x) Ω〈∞, and f:Ω^-× IR be a C^1 function with f(x,s) ≥ 0, V (x,s) ∈Ω ... Let Ω IR^N, (N ≥ 2) be a bounded smooth domain, p is Holder continuous on Ω^-, 1 〈 p^- := inf pΩ(x) ≤ p+ = supp(x) Ω〈∞, and f:Ω^-× IR be a C^1 function with f(x,s) ≥ 0, V (x,s) ∈Ω × R^+ and sup ∈Ωf(x,s) ≤ C(1+s)^q(x), Vs∈IR^+,Vx∈Ω for some 0〈q(x) ∈C(Ω^-) satisfying 1 〈p(x) 〈q(x) ≤p^* (x) -1, Vx ∈Ω ^- and 1 〈 p^- ≤ p^+ ≤ q- ≤ q+. As usual, p* (x) = Np(x)/N-p(x) if p(x) 〈 N and p^* (x) = ∞- if p(x) if p(x) 〉 N. Consider the functional I: W0^1,p(x) (Ω) →IR defined as I(u) def= ∫Ω1/p(x)|△|^p(x)dx-∫ΩF(x,u^+)dx,Vu∈W0^1,p(x)(Ω),where F (x, u) = ∫0^s f (x,s) ds. Theorem 1.1 proves that if u0 ∈ C^1 (Ω^-) is a local minimum of I in the C1 (Ω^-) ∩C0 (Ω^-)) topology, then it is also a local minimum in W0^1,p(x) (Ω)) topology. This result is useful for proving multiple solutions to the associated Euler-lagrange equation (P) defined below. 展开更多
关键词 p (x)-Laplacian equation variational methods local minimizer.
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A Parameter-Free Filled Function for Unconstrained Global Optimization 被引量:9
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作者 安澜 张连生 +2 位作者 陈美霖 Chen mei-lin 《Journal of Shanghai University(English Edition)》 CAS 2004年第2期117-123,共7页
The filled function method is an approach for finding a global minimum of multi-dimensional functions. With more and more relevant research, it becomes a promising way used in unconstrained global optimization. Some f... The filled function method is an approach for finding a global minimum of multi-dimensional functions. With more and more relevant research, it becomes a promising way used in unconstrained global optimization. Some filled functions with one or two parameters have already been suggested. However, there is no certain criterion to choose a parameter appropriately. In this paper, a parameter-free filled function was proposed. The definition of the original filled function and assumptions of the objective function given by Ge were improved according to the presented parameter-free filled function. The algorithm and numerical results of test functions were reported. Conclusions were drawn in the end. Key words global optimization - filled function method - local minimizer MSC 2000 90C30 展开更多
关键词 global optimization filled function method local minimizer
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Two-parameters quasi-filled function algorithm for nonlinear integer programming 被引量:3
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作者 WANG Wei-xiang SHANG You-lin ZHANG Lian-sheng 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第12期2083-2087,共5页
A quasi-filled function for nonlinear integer programming problem is given in this paper. This function contains two parameters which are easily to be chosen. Theoretical properties of the proposed quasi-filled functi... A quasi-filled function for nonlinear integer programming problem is given in this paper. This function contains two parameters which are easily to be chosen. Theoretical properties of the proposed quasi-filled function are investigated. Moreover, we also propose a new solution algorithm using this quasi-filled function to solve nonlinear integer programming problem in this paper. The examples with 2 to 6 variables are tested and computational results indicated the efficiency and reliability of the pro- posed quasi-filled function algorithm. 展开更多
关键词 Integer programming local minimizer Global minimizer Filled function Global optimization
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One-parameter quasi-filled function algorithm for nonlinear integer programming 被引量:2
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作者 尚有林 韩伯顺 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2005年第4期305-310,共6页
A definition of the quasi-filled function for nonlinear integer programming problem is given in this paper. A quasi-filled function satisfying our definition is presented. This function contains only one parameter. Th... A definition of the quasi-filled function for nonlinear integer programming problem is given in this paper. A quasi-filled function satisfying our definition is presented. This function contains only one parameter. The properties of the pro- posed quasi-filled function and the method using this quasi-filled function to solve nonlinear integer programming problem are also discussed in this paper. Numerical results indicated the efficiency and reliability of the proposed quasi-filled function algo- rithm. 展开更多
关键词 Integer programming local minimizer Global minimizer Filled function Global optimization
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A One-parameter Filled Function Method for Nonlinear Integer Programming 被引量:2
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作者 尚有林 杨永建 梁玉梅 《Journal of Donghua University(English Edition)》 EI CAS 2005年第4期1-4,共4页
This paper gives a new definition of the filled function for nonlinear integer programming problem. A filled function satisfying our definition is presented. This function contains only one parameter. The properties o... This paper gives a new definition of the filled function for nonlinear integer programming problem. A filled function satisfying our definition is presented. This function contains only one parameter. The properties of the proposed filled function and the method using this filled function to solve nonlinear integer programming problem are also discussed. Numerical results indicate the efficiency and reliability of the proposed filled function algorithm. 展开更多
关键词 integer programming local minimizer global minimizer filled function global optimization
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A New F-C Function for Box Constrained Global Optimization 被引量:2
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作者 ZHAN Yue SHANG You-lin QU De-qiang 《Chinese Quarterly Journal of Mathematics》 2020年第2期214-220,共7页
To solve the global optimization problems which have several local minimizers,a new F-C function is proposes by combining a lled function and a cross function.The properties of the F-C function are discussed and the c... To solve the global optimization problems which have several local minimizers,a new F-C function is proposes by combining a lled function and a cross function.The properties of the F-C function are discussed and the corresponding algorithm is given in this paper.F-C function has the same local minimizers with the objective function.Therefore,the F-C function method only needs to minimize the objective function once in the rst iteration.Numerical experiments are performed and the results show that the proposed method is very effective. 展开更多
关键词 Global optimization Filled function F-C function local minimizer
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A New Filled Function for Global Optimization Problems with Box Constraints 被引量:2
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作者 QU De-qiang WU Dan SHANG You-lin 《Chinese Quarterly Journal of Mathematics》 2020年第4期354-362,共9页
In this paper, auxiliary function method for global optimization with box constraints is considered. First, a new non-parameter filled function which has the same local minimizers of the objective function is proposed... In this paper, auxiliary function method for global optimization with box constraints is considered. First, a new non-parameter filled function which has the same local minimizers of the objective function is proposed. By the character that having same local minimizers, and these minimizers are all better than the current minimizer of the objective function, it does not need to minimize the objective function except for thefirst iteration in the filled function method. It changes the frame of conventional filled function methods that objective function and filled function are minimized alternately,and can effectively reduce the iterations of the algorithm and accelerate the speed of global optimization. And then the theoretical properties of the filled function are discussed and the corresponding algorithm is established. Finally, numerical experiments are made and comparisons on several test problems are shown which exhibit the feasibility and effectiveness of the algorithm. 展开更多
关键词 Global Optimization Non-Parameter Filled Function local minimizer
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EXACT AUGMENTED LAGRANGIAN FUNCTION FOR NONLINEAR PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS
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作者 杜学武 张连生 +1 位作者 尚有林 李铭明 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第12期1649-1656,共8页
An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstr... An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions, the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, f^om the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented. 展开更多
关键词 local minimizer global minimizer nonlinear programming exact penalty function augmented Lagrangian function
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A REMARK ON THE REGULARITY OF VECTOR-VALUED MAPPINGS DEPENDING ON TWO VARIABLES WHICH MINIMIZE SPLITTING-TYPE VARIATIONAL INTEGRALS
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作者 M. Bildhauer M. Fuchs 《Acta Mathematica Scientia》 SCIE CSCD 2010年第3期963-967,共5页
We combine the maximum principle for vector-valued mappings established by D'Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local mini... We combine the maximum principle for vector-valued mappings established by D'Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local minimizers u: Ω→^R^N of splitting-type variational integrals provided Ω is a domain in R^2. 展开更多
关键词 local minimizers interior regularity anisotropic energies two-dimensional problems
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Insiders' Hedging for Jump Diffusion Processes with Applications to Index Tracking
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作者 苏小囡 王伟 王文胜 《Journal of Donghua University(English Edition)》 EI CAS 2011年第6期571-575,共5页
The hedging problem for insiders is very important in the financial market.The locally risk minimizing hedging was adopted to solve this problem.Since the market was incomplete,the minimal martingale measure was chose... The hedging problem for insiders is very important in the financial market.The locally risk minimizing hedging was adopted to solve this problem.Since the market was incomplete,the minimal martingale measure was chosen as the equivalent martingale measure.By the F-S decomposition,the expression of the locally risk minimizing strategy was presented.Finally,the local risk minimization was applied to index tracking and its relationship with tracking error variance (TEV)-minimizing strategy was obtained. 展开更多
关键词 jump diffusion processes local risk minimization insiders’ hedging index tracking
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Three-dimensional sound source localization using distributed microphone arrays 被引量:3
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作者 KE Wei ZHANG Ming ZHANG Tiecheng 《Chinese Journal of Acoustics》 CSCD 2017年第2期231-244,共14页
To improve the performance of sound source localization based on distributed microphone arrays in noisy and reverberant environments,a sound source localization method was proposed.This method exploited the inherent s... To improve the performance of sound source localization based on distributed microphone arrays in noisy and reverberant environments,a sound source localization method was proposed.This method exploited the inherent spatial sparsity to convert the localization problem into a sparse recovery problem based on the compressive sensing(CS) theory.In this method two-step discrete cosine transform(DCT)-based feature extraction was utilized to cover both short-time and long-time properties of the signal and reduce the dimensions of the sparse model.Moreover,an online dictionary learning(DL) method was used to dynamically adjust the dictionary for matching the changes of audio signals,and then the sparse solution could better represent location estimations.In addition,we proposed an improved approximate l_0norm minimization algorithm to enhance reconstruction performance for sparse signals in low signal-noise ratio(SNR).The effectiveness of the proposed scheme is demonstrated by simulation results where the locations of multiple sources can be obtained in the noisy and reverberant conditions. 展开更多
关键词 localization sparse dictionary minimization noisy dynamically matching approximate utilized audio
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Local Discontinuous Galerkin Method for Parabolic Interface Problems
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作者 Zhi-juan ZHANG Xi-jun YU 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2015年第2期453-466,共14页
In this paper, the minimal dissipation local discontinuous Galerkin method is studied to solve the parabolic interface problems in two-dimensional convex polygonal domains. The interface may be arbitrary smooth curves... In this paper, the minimal dissipation local discontinuous Galerkin method is studied to solve the parabolic interface problems in two-dimensional convex polygonal domains. The interface may be arbitrary smooth curves. The proposed method is proved to be L2 stable and the order of error estimates in the given norm is O(h|logh|^1/2). Numerical experiments show the efficiency and accuracy of the method. 展开更多
关键词 parabolic interface problem minimal dissipation local discontinuous Galerkin method error estimates
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A ONE-PARAMETER FILLED FUNCTION FOR NONSMOOTH GLOBAL OPTIMIZATION AND ITS APPLICATION 被引量:1
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作者 Ying ZHANG Liansheng ZHANG Yingtao XU 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2010年第6期1195-1209,共15页
This paper presents a modified definition of the filled function for finding a global minimizer of a nonsmooth function on a closed bounded set, and then give a one-parameter filled function. Theoretical and numerical... This paper presents a modified definition of the filled function for finding a global minimizer of a nonsmooth function on a closed bounded set, and then give a one-parameter filled function. Theoretical and numerical properties of the proposed filled function are investigated and a corresponding solution algorithm is proposed. The proposed filled function's parameter is easier to be appropriately chosen than previous functions in literatures. Numerical results obtained indicate the efficiency of the proposed filled function method. An improved fingerprint recognition method using global filled function is also reported. 展开更多
关键词 Filled function global minimizer global optimization local minimizer nonsmooth optimization.
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Nonconvex Sorted l1 Minimization for Sparse Approximation 被引量:1
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作者 Xiao-Lin Huang Lei Shi Ming Yan 《Journal of the Operations Research Society of China》 EI CSCD 2015年第2期207-229,共23页
The l1 norm is the tight convex relaxation for the l0 norm and has been successfully applied for recovering sparse signals.However,for problems with fewer samples than required for accurate l1 recovery,one needs to ap... The l1 norm is the tight convex relaxation for the l0 norm and has been successfully applied for recovering sparse signals.However,for problems with fewer samples than required for accurate l1 recovery,one needs to apply nonconvex penalties such as lp norm.As one method for solving lp minimization problems,iteratively reweighted l1 minimization updates the weight for each component based on the value of the same component at the previous iteration.It assigns large weights on small components in magnitude and small weights on large components in magnitude.The set of the weights is not fixed,and it makes the analysis of this method difficult.In this paper,we consider a weighted l1 penalty with the set of the weights fixed,and the weights are assigned based on the sort of all the components in magnitude.The smallest weight is assigned to the largest component in magnitude.This new penalty is called nonconvex sorted l1.Then we propose two methods for solving nonconvex sorted l1 minimization problems:iteratively reweighted l1 minimization and iterative sorted thresholding,and prove that both methods will converge to a local minimizer of the nonconvex sorted l1 minimization problems.We also show that both methods are generalizations of iterative support detection and iterative hard thresholding,respectively.The numerical experiments demonstrate the better performance of assigning weights by sort compared to assigning by value. 展开更多
关键词 Iteratively reweighted1 minimization Iterative sorted thresholding local minimizer Nonconvex optimization Sparse approximation
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SECOND-ORDER CONVERGENCE PROPERTIES OF TRUST-REGION METHODS USING INCOMPLETE CURVATURE INFORMATION, WITH AN APPLICATION TO MULTIGRID OPTIMIZATION 被引量:1
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作者 Serge Gratton Annick Sartenaer Philippe L. Toint 《Journal of Computational Mathematics》 SCIE CSCD 2006年第6期676-692,共17页
Convergence properties of trust-region methods for unconstrained nonconvex optimization is considered in the case where information on the objective function's local curvature is incomplete, in the sense that it may ... Convergence properties of trust-region methods for unconstrained nonconvex optimization is considered in the case where information on the objective function's local curvature is incomplete, in the sense that it may be restricted to a fixed set of "test directions" and may not be available at every iteration. It is shown that convergence to local "weak" minimizers can still be obtained under some additional but algorithmically realistic conditions. These theoretical results are then applied to recursive multigrid trust-region methods, which suggests a new class of algorithms with guaranteed second-order convergence properties. 展开更多
关键词 Nonlinear optimization Convergence to local minimizers Multilevel problems.
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A Class of Parameter-free Filled Functions for Box-constrained System of Nonlinear Equations
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作者 Liu-yang YUAN Zhong-ping WAN +1 位作者 Qiu-hua TANG Yue ZHENG 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2016年第2期355-364,共10页
In this paper, a class of parameter-free filled functions is proposed for solving box-constrained system of nonlinear equations. Firstly, the original problem is converted into an equivalent global optimization proble... In this paper, a class of parameter-free filled functions is proposed for solving box-constrained system of nonlinear equations. Firstly, the original problem is converted into an equivalent global optimization problem. Subsequently, a class of parameter-free filled functions is proposed for solving the problem. Some properties of the new class of filled functions are studied and discussed. Finally, an algorithm which neither computes nor explicitly approximates gradients during minimizing the filled functions is presented. The global convergence of the algorithm is also established. The implementation of the algorithm on several test problems is reported with satisfactory numerical results. 展开更多
关键词 system of nonlinear equations global optimization filled function method local minimizer globalminimizer
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