A class of discontinuous penalty functions was proposed to solve constrained minimization problems with the integral approach to global optimization, m-mean value and v-variance optimality conditions of a constrained ...A class of discontinuous penalty functions was proposed to solve constrained minimization problems with the integral approach to global optimization, m-mean value and v-variance optimality conditions of a constrained and penalized minimization problem were investigated. A nonsequential algorithm was proposed. Numerical examples were given to illustrate the effectiveness of the algorithm.展开更多
Global minimization algorithm is indispensable for solving protein folding problems based on thermodynamic hypothesis. A contact difference (CD) based on pseudo potential function, for simulating empirical contact p...Global minimization algorithm is indispensable for solving protein folding problems based on thermodynamic hypothesis. A contact difference (CD) based on pseudo potential function, for simulating empirical contact potential functions and testing global minimization algorithm was proposed. The present article describes a conformational sampiing and global minimization algorithm, which is called WL, based on Monte Carlo simulation and simulated annealing. It can be used to locate CD's globe minimum and refold extended protein structures, as small as 0. 03 nm, from the native structures, back to ones with root mean square distance(RMSD). These results demonstrate that the global minimization problems for empirical contact potential functions may be solvable.展开更多
Global minimization algorithm is indispensable to solving the protein folding problem based upon thermodynamic hypothesis. Here we propose a pseudo potential function, contact difference(CD), for simulating empirical ...Global minimization algorithm is indispensable to solving the protein folding problem based upon thermodynamic hypothesis. Here we propose a pseudo potential function, contact difference(CD), for simulating empirical contact potential functions and testing global minimization algorithm. The present paper covers conformational sampling and global minimization algorithm called BML03, based upon Monte Carlo and simulated annealing, which is able to locate CD′s global minimum and refold extended protein structures into ones with root mean square distance(RMSD) as small as 0.03 nm from the native structures. For empirical contact potential functions, these results demonstrate that their global minimization problems may be solvable.展开更多
In this Paper we continue to investigate global minimization problems. An integral approach is applied to treat a global minimization problem of a discontinuous function. With the help ofthe theory of measure (Q-measu...In this Paper we continue to investigate global minimization problems. An integral approach is applied to treat a global minimization problem of a discontinuous function. With the help ofthe theory of measure (Q-measure) and integration, optimality conditions of a robust function over arobust set are derived. Algorithms and their implementations for finding global minima are proposed.Numerical tests and applications show that the algorithms are effective.展开更多
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
This paper considers the concave minimization problem with linear constrailits,proposes a technique which may avoid the unsuitable Karush-Kuhn-Tucker poiats,then combines this technique with nank-Wolfe method and simp...This paper considers the concave minimization problem with linear constrailits,proposes a technique which may avoid the unsuitable Karush-Kuhn-Tucker poiats,then combines this technique with nank-Wolfe method and simplex method to form a pivoting method which can determine a strictly local minimizer of the problem in a finite number of iterations. Basing on strictly local minimizers, a new cutting plane method is proposed. Under some mild conditions, the new cutting plane method is proved to be finitely terminated at an θ-global minimizer of the problem.展开更多
Various approaches have been developed for solving a variety of continuous global optimization problems. But up to now, less work has been devoted to solving nonlinear integer programming problems due to the inherent...Various approaches have been developed for solving a variety of continuous global optimization problems. But up to now, less work has been devoted to solving nonlinear integer programming problems due to the inherent difficulty. This paper manages to transform the general nonlinear integer programming problem into an equivalent' special continuous global minimization problem. Thus any effective global optimization algorithm can be used to solve nonlinear integer programming problems. This result will also promote the research on global optimization. We present an interval Branch-and-Bound algorithm. Numerical experiments show that this approach is efficient. (Author abstract) 11 Refs.展开更多
The Filled Function Method is a class of effective algorithms for continuous global optimization. In this paper, a new filled function method is introduced and used to solve integer programming. Firstly, some basic de...The Filled Function Method is a class of effective algorithms for continuous global optimization. In this paper, a new filled function method is introduced and used to solve integer programming. Firstly, some basic definitions of discrete optimization are given. Then an algorithm and the implementation of this algorithm on several test problems are showed. The computational results show the algorithm is effective.展开更多
Focuses on a study which determined the geometry meaning of the maxima of the CDT mathematical subproblem's dual function. Properties of trust region subproblem; Approximation of the CDT feasible region; Relations...Focuses on a study which determined the geometry meaning of the maxima of the CDT mathematical subproblem's dual function. Properties of trust region subproblem; Approximation of the CDT feasible region; Relations between the CDT problem and the trust region problem; Illustration of the geometry meaning of the jump parameter.展开更多
In this paper, we discuss the vortex structure of the superconducting thin films placed in a magnetic field. We show that the global minimizer of the functional modelling the superconducting thin films has a bounded n...In this paper, we discuss the vortex structure of the superconducting thin films placed in a magnetic field. We show that the global minimizer of the functional modelling the superconducting thin films has a bounded number of vortices when the applied magnetic field hex 〈 Hc1 + K log | logε| where Hc1 is the lower critical field of the film obtained by Ding and Du in SIAM J. Math. Anal., 2002. The locations of the vortices are also given.展开更多
Recently, the matrix factorization model attracts increasing attentions in handling large-scale rank minimization problems, which is essentially a nonconvex minimization problem. Specifically, it is a quadratic least ...Recently, the matrix factorization model attracts increasing attentions in handling large-scale rank minimization problems, which is essentially a nonconvex minimization problem. Specifically, it is a quadratic least squares problem and consequently a quartic polynomial optimization problem. In this paper, we introduce a concept of the SNIG ("Second-order Necessary optimality Implies Global optimality") condition which stands for the property that any second-order stationary point of the matrix factorization model must be a global minimizer. Some scenarios under which the SNIG condition holds are presented. Furthermore, we illustrate by an example when the SNIG condition may fail.展开更多
文摘A class of discontinuous penalty functions was proposed to solve constrained minimization problems with the integral approach to global optimization, m-mean value and v-variance optimality conditions of a constrained and penalized minimization problem were investigated. A nonsequential algorithm was proposed. Numerical examples were given to illustrate the effectiveness of the algorithm.
文摘Global minimization algorithm is indispensable for solving protein folding problems based on thermodynamic hypothesis. A contact difference (CD) based on pseudo potential function, for simulating empirical contact potential functions and testing global minimization algorithm was proposed. The present article describes a conformational sampiing and global minimization algorithm, which is called WL, based on Monte Carlo simulation and simulated annealing. It can be used to locate CD's globe minimum and refold extended protein structures, as small as 0. 03 nm, from the native structures, back to ones with root mean square distance(RMSD). These results demonstrate that the global minimization problems for empirical contact potential functions may be solvable.
基金Supported by the National Natural Science Foundation of China(No.30 2 4 0 0 16)
文摘Global minimization algorithm is indispensable to solving the protein folding problem based upon thermodynamic hypothesis. Here we propose a pseudo potential function, contact difference(CD), for simulating empirical contact potential functions and testing global minimization algorithm. The present paper covers conformational sampling and global minimization algorithm called BML03, based upon Monte Carlo and simulated annealing, which is able to locate CD′s global minimum and refold extended protein structures into ones with root mean square distance(RMSD) as small as 0.03 nm from the native structures. For empirical contact potential functions, these results demonstrate that their global minimization problems may be solvable.
基金Project supported by National Natural Science Foundation of China
文摘In this Paper we continue to investigate global minimization problems. An integral approach is applied to treat a global minimization problem of a discontinuous function. With the help ofthe theory of measure (Q-measure) and integration, optimality conditions of a robust function over arobust set are derived. Algorithms and their implementations for finding global minima are proposed.Numerical tests and applications show that the algorithms are effective.
文摘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.
文摘This paper considers the concave minimization problem with linear constrailits,proposes a technique which may avoid the unsuitable Karush-Kuhn-Tucker poiats,then combines this technique with nank-Wolfe method and simplex method to form a pivoting method which can determine a strictly local minimizer of the problem in a finite number of iterations. Basing on strictly local minimizers, a new cutting plane method is proposed. Under some mild conditions, the new cutting plane method is proved to be finitely terminated at an θ-global minimizer of the problem.
文摘Various approaches have been developed for solving a variety of continuous global optimization problems. But up to now, less work has been devoted to solving nonlinear integer programming problems due to the inherent difficulty. This paper manages to transform the general nonlinear integer programming problem into an equivalent' special continuous global minimization problem. Thus any effective global optimization algorithm can be used to solve nonlinear integer programming problems. This result will also promote the research on global optimization. We present an interval Branch-and-Bound algorithm. Numerical experiments show that this approach is efficient. (Author abstract) 11 Refs.
基金Foundation item: the National Science Foundation of China(7A14178) the Science Fund of Shanghai University of Engineering Science for Young Scholars(2005Q23) the Natural Science Foundation of Education Commission of Shanghai (No.05NZ07).
文摘The Filled Function Method is a class of effective algorithms for continuous global optimization. In this paper, a new filled function method is introduced and used to solve integer programming. Firstly, some basic definitions of discrete optimization are given. Then an algorithm and the implementation of this algorithm on several test problems are showed. The computational results show the algorithm is effective.
基金Research partially supported by Chinese NSF grants 19525101, 19731010 and State key project 96-221-04-02-02.
文摘Focuses on a study which determined the geometry meaning of the maxima of the CDT mathematical subproblem's dual function. Properties of trust region subproblem; Approximation of the CDT feasible region; Relations between the CDT problem and the trust region problem; Illustration of the geometry meaning of the jump parameter.
基金partially supported by the Natural Science Foundation of China (Nos. 19971030, 10471050)the Natural Science Foundation of Guangdong Province (No. 000671, No. 031495)partially supported by a grant from HKRGC
文摘In this paper, we discuss the vortex structure of the superconducting thin films placed in a magnetic field. We show that the global minimizer of the functional modelling the superconducting thin films has a bounded number of vortices when the applied magnetic field hex 〈 Hc1 + K log | logε| where Hc1 is the lower critical field of the film obtained by Ding and Du in SIAM J. Math. Anal., 2002. The locations of the vortices are also given.
文摘Recently, the matrix factorization model attracts increasing attentions in handling large-scale rank minimization problems, which is essentially a nonconvex minimization problem. Specifically, it is a quadratic least squares problem and consequently a quartic polynomial optimization problem. In this paper, we introduce a concept of the SNIG ("Second-order Necessary optimality Implies Global optimality") condition which stands for the property that any second-order stationary point of the matrix factorization model must be a global minimizer. Some scenarios under which the SNIG condition holds are presented. Furthermore, we illustrate by an example when the SNIG condition may fail.