To determine whether a given deterministic nonlinear dynamic system is chaotic or periodic, a novel test approach named zero-one （0-1） test has been proposed recently. In this approach, the regular and chaotic motio...To determine whether a given deterministic nonlinear dynamic system is chaotic or periodic, a novel test approach named zero-one （0-1） test has been proposed recently. In this approach, the regular and chaotic motions can be decided by calculating the parameter K approaching asymptotically to zero or one. In this study, we focus on the 0-1 test algorithm and illustrate the selection of parameters of this algorithm by numerical experiments. To validate the reliability and the universality of this algorithm, it is applied to typical nonlinear dynamic systems, including fractional-order dynamic system.展开更多
In this paper, a branch-and-bound method for solving multi-dimensional quadratic 0-1 knapsack problems was studied. The method was based on the Lagrangian relaxation and the surrogate constraint technique for finding ...In this paper, a branch-and-bound method for solving multi-dimensional quadratic 0-1 knapsack problems was studied. The method was based on the Lagrangian relaxation and the surrogate constraint technique for finding feasible solutions. The Lagrangian relaxations were solved with the maximum-flow algorithm and the Lagrangian bounds was determined with the outer approximation method. Computational results show the efficiency of the proposed method for multi-dimensional quadratic 0-1 knapsack problems.展开更多
In this paper, disturbed sparse linear equations over the 0-1 finite field are considered. Due to the special structure of the problem, the standard alternating coordinate method can be implemented in such a way to yi...In this paper, disturbed sparse linear equations over the 0-1 finite field are considered. Due to the special structure of the problem, the standard alternating coordinate method can be implemented in such a way to yield a fast and efficient algorithm. Our alternating coordinate algorithm makes use of the sparsity of the coefficient matrix and the current residuals of the equations. Some hybrid techniques such as random restarts and genetic crossovers are also applied to improve our algorithm.展开更多
Mathematical programming problems with semi-continuous variables and cardinality constraint have many applications,including production planning,portfolio selection,compressed sensing and subset selection in regressio...Mathematical programming problems with semi-continuous variables and cardinality constraint have many applications,including production planning,portfolio selection,compressed sensing and subset selection in regression.This class of problems can be modeled as mixed-integer programs with special structures and are in general NP-hard.In the past few years,based on new reformulations,approximation and relaxation techniques,promising exact and approximate methods have been developed.We survey in this paper these recent developments for this challenging class of mathematical programming problems.展开更多
基金Project supported by the National Natural Science Foundation of of China (Grant No. 60672041)
文摘To determine whether a given deterministic nonlinear dynamic system is chaotic or periodic, a novel test approach named zero-one （0-1） test has been proposed recently. In this approach, the regular and chaotic motions can be decided by calculating the parameter K approaching asymptotically to zero or one. In this study, we focus on the 0-1 test algorithm and illustrate the selection of parameters of this algorithm by numerical experiments. To validate the reliability and the universality of this algorithm, it is applied to typical nonlinear dynamic systems, including fractional-order dynamic system.
基金Project supported by the National Natural Science Foundation of China （Grant No.10571116）
文摘In this paper, a branch-and-bound method for solving multi-dimensional quadratic 0-1 knapsack problems was studied. The method was based on the Lagrangian relaxation and the surrogate constraint technique for finding feasible solutions. The Lagrangian relaxations were solved with the maximum-flow algorithm and the Lagrangian bounds was determined with the outer approximation method. Computational results show the efficiency of the proposed method for multi-dimensional quadratic 0-1 knapsack problems.
文摘In this paper, disturbed sparse linear equations over the 0-1 finite field are considered. Due to the special structure of the problem, the standard alternating coordinate method can be implemented in such a way to yield a fast and efficient algorithm. Our alternating coordinate algorithm makes use of the sparsity of the coefficient matrix and the current residuals of the equations. Some hybrid techniques such as random restarts and genetic crossovers are also applied to improve our algorithm.
基金supported by the National Natural Science Foundation of China grants(Nos.11101092,10971034)the Joint National Natural Science Foundation of China/Research Grants Council of Hong Kong grant(No.71061160506)the Research Grants Council of Hong Kong grants(Nos.CUHK414808 and CUHK414610).
文摘Mathematical programming problems with semi-continuous variables and cardinality constraint have many applications,including production planning,portfolio selection,compressed sensing and subset selection in regression.This class of problems can be modeled as mixed-integer programs with special structures and are in general NP-hard.In the past few years,based on new reformulations,approximation and relaxation techniques,promising exact and approximate methods have been developed.We survey in this paper these recent developments for this challenging class of mathematical programming problems.
