In this paper, a new algorithm-approximate penalty function method is designed, which can be used to solve a bilevel optimization problem with linear constrained function. In this kind of bilevel optimization problem....In this paper, a new algorithm-approximate penalty function method is designed, which can be used to solve a bilevel optimization problem with linear constrained function. In this kind of bilevel optimization problem. the evaluation of the objective function is very difficult, so that only their approximate values can be obtained. This algorithm is obtained by combining penalty function method and approximation in bilevel programming. The presented algorithm is completely different from existing methods. That convergence for this algorithm is proved.展开更多
By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constra...By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constraints in Karush-Kuhn-Tucker necessary conditions are removed. For constructing the Lagrange neural network and Lagrange multiplier method, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse those results dedicated to equality constraints, and they can be similarly proved with minor modification. Utilizing this technique, a new type of Lagrange neural network and a new type of Lagrange multiplier method are devised, which both handle inequality constraints directly. Also, their stability and convergence are analyzed rigorously.展开更多
The rigid-plastic analysis of mental forming simulation is formulated as a discrete nonlinear mathematical programming problem with equality and inequality constraints by means of the finite element technique. An iter...The rigid-plastic analysis of mental forming simulation is formulated as a discrete nonlinear mathematical programming problem with equality and inequality constraints by means of the finite element technique. An iteration algorithm is used to solve this formulation, which distinguishes the integration points of the rigid zones and the plastic zones and solves a series of the quadratic programming to overcome the difficulties caused by the nonsmoothness and the nonlinearity of the objective function. This method has been used to carry out the rigid-plastic FEM analysis. An example is given to demonstrate the effectiveness of this method.展开更多
A novel slow-down set waveform is proposed to improve the set performance and a 1 kb phase change random access memory chip fabricated with a 13nm CMOS technology is implemented to investigate the set performance by d...A novel slow-down set waveform is proposed to improve the set performance and a 1 kb phase change random access memory chip fabricated with a 13nm CMOS technology is implemented to investigate the set performance by different set programming strategies based on this new set pulse. The amplitude difference （I1 - I2） of the set pulse is proved to be a crucial parameter for set programming. We observe and analyze the cell characteristics with different I1 - I2 by means of thermal simulations and high-resolution transmission electron microscopy, which reveal that an incomplete set programming will occur when the proposed slow-down pulse is set with an improperly high I1 - I2. This will lead to an amorphous residue in the active region. We also discuss the programming method to avoid the set performance degradations.展开更多
In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space w...In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.展开更多
In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method,a class of new restarting three terms conjugate gradient methods is presented.Global conv...In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method,a class of new restarting three terms conjugate gradient methods is presented.Global convergence properties of the new method with two kinds of common line searches are proved.展开更多
To solve vehicle routing problem with different fleets, two methodologies are developed. The first methodology adopts twophase strategy. In the first phase, the improved savings method is used to assign customers to a...To solve vehicle routing problem with different fleets, two methodologies are developed. The first methodology adopts twophase strategy. In the first phase, the improved savings method is used to assign customers to appropriate vehicles. In the second phase, the iterated dynasearch algorithm is adopted to route each selected vehicle with the assigned customers. The iterated dynasearch algorithm combines dynasearch algorithm with iterated local search algorithm based on random kicks. The second methodplogy adopts the idea of cyclic transfer which is performed by using dynamic programming algorithm, and the iterated dynasearch algorithm is also embedded in it. The test results show that both methodologies generate better solutions than the traditional method, and the second methodology is superior to the first one.展开更多
We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the s...We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based Mehrotra-type algorithm for linear programming, that was proposed by Salahi et al. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O（r log ε1） iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of Mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples.展开更多
This study investigated the application and the effect of Group Investigation(GI) in the College English Program in a Chinese University. A qualitative case study method was used to understand the GI system used by Ch...This study investigated the application and the effect of Group Investigation(GI) in the College English Program in a Chinese University. A qualitative case study method was used to understand the GI system used by Chinese instructors as well as the achievements acquired and challenges met by the participants. Three instructors and fifteen second-year-undergraduates taking a course titled Sources of European Culture participated. Interviews, observations, and documents were used to collect the data. Data analysis showed Chinese instructors applied a GI technique similar to that discussed by Johnson and Johnson(1999); however, GI in the Chinese context demanded more effort from the teacher for designing tasks and provided help in modeling uses of English and in preparing visual, especially Power Point, presentations. Although participants used their mother tongue at some stages, their autonomy over English learning was activated, and horizons in the course content were broadened.展开更多
In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Comb...In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.展开更多
In contrast to most existing works on robust unit commitment(UC),this study proposes a novel big-M-based mixed-integer linear programming(MILP)method to solve security-constrained UC problems considering the allowable...In contrast to most existing works on robust unit commitment(UC),this study proposes a novel big-M-based mixed-integer linear programming(MILP)method to solve security-constrained UC problems considering the allowable wind power output interval and its adjustable conservativeness.The wind power accommodation capability is usually limited by spinning reserve requirements and transmission line capacity in power systems with large-scale wind power integration.Therefore,by employing the big-M method and adding auxiliary 0-1 binary variables to describe the allowable wind power output interval,a bilinear programming problem meeting the security constraints of system operation is presented.Furthermore,an adjustable confidence level was introduced into the proposed robust optimization model to decrease the level of conservatism of the robust solutions.This can establish a trade-off between economy and security.To develop an MILP problem that can be solved by commercial solvers such as CPLEX,the big-M method is utilized again to represent the bilinear formulation as a series of linear inequality constraints and approximately address the nonlinear formulation caused by the adjustable conservativeness.Simulation studies on a modified IEEE 26-generator reliability test system connected to wind farms were performed to confirm the effectiveness and advantages of the proposed method.展开更多
Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS met...Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991), a class of new restarting conjugate gradient methods is presented. Global convergences of the new method with two kinds of common line searches, are proved. Firstly, it is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously dif ferentiable function with Curry-Altman's step size rule and a bounded level set. Secondly, by using comparing technique, some general convergence properties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method.展开更多
The paper presents a formal and practical approach to dependable algorithm development.First,starting from a formal specification based on the Eindhoven quantifier notation,a problem is regularly reduced to subproblem...The paper presents a formal and practical approach to dependable algorithm development.First,starting from a formal specification based on the Eindhoven quantifier notation,a problem is regularly reduced to subproblems with less complexity by using a concise set of calculation rules,the result of which establishes a recurrence-based algorithm.Second,a loop invariant is derived from the problem specification and recurrence,which certifies the transformation from the recurrence-based algorithm to one or more iterative programs.We demonstrate that our approach covers a number of classical algorithm design tactics,develops algorithmic programs together with their proof of correctness,and thus contributes fundamentally to the dependability of computer software.展开更多
文摘In this paper, a new algorithm-approximate penalty function method is designed, which can be used to solve a bilevel optimization problem with linear constrained function. In this kind of bilevel optimization problem. the evaluation of the objective function is very difficult, so that only their approximate values can be obtained. This algorithm is obtained by combining penalty function method and approximation in bilevel programming. The presented algorithm is completely different from existing methods. That convergence for this algorithm is proved.
文摘By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constraints in Karush-Kuhn-Tucker necessary conditions are removed. For constructing the Lagrange neural network and Lagrange multiplier method, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse those results dedicated to equality constraints, and they can be similarly proved with minor modification. Utilizing this technique, a new type of Lagrange neural network and a new type of Lagrange multiplier method are devised, which both handle inequality constraints directly. Also, their stability and convergence are analyzed rigorously.
文摘The rigid-plastic analysis of mental forming simulation is formulated as a discrete nonlinear mathematical programming problem with equality and inequality constraints by means of the finite element technique. An iteration algorithm is used to solve this formulation, which distinguishes the integration points of the rigid zones and the plastic zones and solves a series of the quadratic programming to overcome the difficulties caused by the nonsmoothness and the nonlinearity of the objective function. This method has been used to carry out the rigid-plastic FEM analysis. An example is given to demonstrate the effectiveness of this method.
基金Supported by the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No XDA09020402the National Key Basic Research Program of China under Grant Nos 2013CBA01900,2010CB934300,2011CBA00607,and 2011CB932804+2 种基金the National Integrate Circuit Research Program of China under Grant No 2009ZX02023-003the National Natural Science Foundation of China under Grant Nos 61176122,61106001,61261160500,and 61376006the Science and Technology Council of Shanghai under Grant Nos 12nm0503701,13DZ2295700,12QA1403900,and 13ZR1447200
文摘A novel slow-down set waveform is proposed to improve the set performance and a 1 kb phase change random access memory chip fabricated with a 13nm CMOS technology is implemented to investigate the set performance by different set programming strategies based on this new set pulse. The amplitude difference （I1 - I2） of the set pulse is proved to be a crucial parameter for set programming. We observe and analyze the cell characteristics with different I1 - I2 by means of thermal simulations and high-resolution transmission electron microscopy, which reveal that an incomplete set programming will occur when the proposed slow-down pulse is set with an improperly high I1 - I2. This will lead to an amorphous residue in the active region. We also discuss the programming method to avoid the set performance degradations.
基金supported by the National Natural Science Foundation of China(11401126,71471140 and 11361018)Guangxi Natural Science Foundation(2016GXNSFBA380102 and 2014GXNSFFA118001)+2 种基金Guangxi Key Laboratory of Cryptography and Information Security(GCIS201618)Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(YQ15112 and YQ16112)China
文摘In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.
基金Supported by the National Natural Science Foundation of China（10571106） Supported by the Fundamental Research Funds for the Central Universities（10CX04044A）
文摘In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method,a class of new restarting three terms conjugate gradient methods is presented.Global convergence properties of the new method with two kinds of common line searches are proved.
基金The National Natural Science Founda-tion of China ( No.70471039)the National Social Science Foundation of China (No.07BJY038)the Program for New Century Excellent Talents in University (No.NCET-04-0886)
文摘To solve vehicle routing problem with different fleets, two methodologies are developed. The first methodology adopts twophase strategy. In the first phase, the improved savings method is used to assign customers to appropriate vehicles. In the second phase, the iterated dynasearch algorithm is adopted to route each selected vehicle with the assigned customers. The iterated dynasearch algorithm combines dynasearch algorithm with iterated local search algorithm based on random kicks. The second methodplogy adopts the idea of cyclic transfer which is performed by using dynamic programming algorithm, and the iterated dynasearch algorithm is also embedded in it. The test results show that both methodologies generate better solutions than the traditional method, and the second methodology is superior to the first one.
基金Supported by the National Natural Science Foundation of China(11471102,61301229)Supported by the Natural Science Foundation of Henan University of Science and Technology(2014QN039)
文摘We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based Mehrotra-type algorithm for linear programming, that was proposed by Salahi et al. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O（r log ε1） iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of Mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples.
基金supported by the 2013 Fundamental Re-search Funds for the Central Universities of Xi’an Jiaotong UniversityThe Subject of Shaanxi Province Educational Science Twelveth-Five-Year Plan
文摘This study investigated the application and the effect of Group Investigation(GI) in the College English Program in a Chinese University. A qualitative case study method was used to understand the GI system used by Chinese instructors as well as the achievements acquired and challenges met by the participants. Three instructors and fifteen second-year-undergraduates taking a course titled Sources of European Culture participated. Interviews, observations, and documents were used to collect the data. Data analysis showed Chinese instructors applied a GI technique similar to that discussed by Johnson and Johnson(1999); however, GI in the Chinese context demanded more effort from the teacher for designing tasks and provided help in modeling uses of English and in preparing visual, especially Power Point, presentations. Although participants used their mother tongue at some stages, their autonomy over English learning was activated, and horizons in the course content were broadened.
文摘In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.
基金State Grid Jiangsu Electric Power Co.,Ltd(JF2020001)National Key Technology R&D Program of China(2017YFB0903300)State Grid Corporation of China(521OEF17001C).
文摘In contrast to most existing works on robust unit commitment(UC),this study proposes a novel big-M-based mixed-integer linear programming(MILP)method to solve security-constrained UC problems considering the allowable wind power output interval and its adjustable conservativeness.The wind power accommodation capability is usually limited by spinning reserve requirements and transmission line capacity in power systems with large-scale wind power integration.Therefore,by employing the big-M method and adding auxiliary 0-1 binary variables to describe the allowable wind power output interval,a bilinear programming problem meeting the security constraints of system operation is presented.Furthermore,an adjustable confidence level was introduced into the proposed robust optimization model to decrease the level of conservatism of the robust solutions.This can establish a trade-off between economy and security.To develop an MILP problem that can be solved by commercial solvers such as CPLEX,the big-M method is utilized again to represent the bilinear formulation as a series of linear inequality constraints and approximately address the nonlinear formulation caused by the adjustable conservativeness.Simulation studies on a modified IEEE 26-generator reliability test system connected to wind farms were performed to confirm the effectiveness and advantages of the proposed method.
文摘Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991), a class of new restarting conjugate gradient methods is presented. Global convergences of the new method with two kinds of common line searches, are proved. Firstly, it is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously dif ferentiable function with Curry-Altman's step size rule and a bounded level set. Secondly, by using comparing technique, some general convergence properties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method.
基金National Natural Science Foundation of China under Grant No. 60773054,60870002 and 61020106009Zhejiang Provincial Natural Science Foundation of China under Grant No. R1110679
文摘The paper presents a formal and practical approach to dependable algorithm development.First,starting from a formal specification based on the Eindhoven quantifier notation,a problem is regularly reduced to subproblems with less complexity by using a concise set of calculation rules,the result of which establishes a recurrence-based algorithm.Second,a loop invariant is derived from the problem specification and recurrence,which certifies the transformation from the recurrence-based algorithm to one or more iterative programs.We demonstrate that our approach covers a number of classical algorithm design tactics,develops algorithmic programs together with their proof of correctness,and thus contributes fundamentally to the dependability of computer software.
