This article presents an application of generalized pattern search （PS） algorithm to solve economic load dispatch （ELD） problems with convex and non-convex fuel cost objective functions. Main objective of ELI） is...This article presents an application of generalized pattern search （PS） algorithm to solve economic load dispatch （ELD） problems with convex and non-convex fuel cost objective functions. Main objective of ELI） is to determine the most economic generating dispatch required to satisfy the predicted load demands including line losses. Relaxing various equality and inequality constraints are considered. The unit operation minhnum/maximum constraints, effects of valve-point and line losses are considered for the practical applications. Several case studies were tested and verified, which indicate an improvement in total fuel cost savings. The robustness of the proposed PS method have been assessed and investigated through intensive comparisons with reported results in recent researches. The results are very encouraging and suggesting that PS may be very useful tool in solving power system ELD problems.展开更多
By handling the travel cost function artfully, the authors formulate the transportation mixed network design problem （MNDP） as a mixed-integer, nonlinear bilevel programming problem, in which the lower-level problem...By handling the travel cost function artfully, the authors formulate the transportation mixed network design problem （MNDP） as a mixed-integer, nonlinear bilevel programming problem, in which the lower-level problem, comparing with that of conventional bilevel DNDP models, is not a side constrained user equilibrium assignment problem, but a standard user equilibrium assignment problem. Then, the bilevel programming model for MNDP is reformulated as a continuous version of bilevel programming problem by the continuation method. By virtue of the optimal-value function, the lower-level assignment problem can be expressed as a nonlinear equality constraint. Therefore, the bilevel programming model for MNDP can be transformed into an equivalent single-level optimization problem. By exploring the inherent nature of the MNDP, the optimal-value function for the lower- level equilibrium assignment problem is proved to be continuously differentiable and its functional value and gradient can be obtained efficiently. Thus, a continuously differentiable but still nonconvex optimization formulation of the MNDP is created, and then a locally convergent algorithm is proposed by applying penalty function method. The inner loop of solving the subproblem is mainly to implement an Ml-or-nothing assignment. Finally, a small-scale transportation network and a large-scale network are presented to verify the proposed model and algorithm.展开更多
This paper proposes a nonmonotone line search filter method with reduced Hessian updating for solving nonlinear equality constrained optimization.In order to deal with large scale problems,a reduced Hessian matrix is ...This paper proposes a nonmonotone line search filter method with reduced Hessian updating for solving nonlinear equality constrained optimization.In order to deal with large scale problems,a reduced Hessian matrix is approximated by BFGS updates.The new method assures global convergence without using a merit function.By Lagrangian function in the filter and nonmonotone scheme,the authors prove that the method can overcome Maratos effect without using second order correction step so that the locally superlinear convergence is achieved.The primary numerical experiments are reported to show effectiveness of the proposed algorithm.展开更多
The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty fu...The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty function with two penalty parameters for inequality constrained bilevel programming. Under some conditions, the optimal solution to the bilevel programming defined by the quadratic objective penalty function is proved to be an optimal solution to the original bilevel programming. Moreover, based on the quadratic objective penalty function, an algorithm is developed to l^nd an optimal solution to the original bilevel programming, and its convergence proved under some conditions. Furthermore, under the assumption of convexity at function without lower level problems is defined and lower level problems, a quadratic objective penalty is proved equal to the original bilevel programming.展开更多
Let β 〉 0 and Sβ ：= {z ∈ C ： ｜Imz｜ 〈β} be a strip in the complex plane. For an integer r ≥ 0, let H∞^Г,β denote those real-valued functions f on R, which are analytic in Sβ and satisfy the restriction ...Let β 〉 0 and Sβ ：= {z ∈ C ： ｜Imz｜ 〈β} be a strip in the complex plane. For an integer r ≥ 0, let H∞^Г,β denote those real-valued functions f on R, which are analytic in Sβ and satisfy the restriction ｜f^（r）（z）｜ ≤ 1, z ∈ Sβ. For σ 〉 0, denote by Bσ the class of functions f which have spectra in （-2πσ, 2πσ）. And let Bσ^⊥ be the class of functions f which have no spectrum in （-2πσ, 2πσ）. We prove an inequality of Bohr type‖f‖∞≤π/√λ∧σ^r∑k=0^∞（-1）^k（r＋1）/（2k＋1）^rsinh（（2k＋1）2σβ）,f∈H∞^r,β∩B1/σ,where λ∈（0,1）,∧and ∧′are the complete elliptic integrals of the first kind for the moduli λ and λ′=√1- λ^2,respectively,and λ satisfies4∧β/π∧′=1/σ.The constant in the above inequality is exact.展开更多
This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,......This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,..., xn] and a finite subset H of R[x1,..., xn], denote by V(f : H) the set {f( ˉα) | ˉα∈ Rn, and h( ˉα) =0, ? h ∈ H}. We provide an effective algorithm for computing a finite set U of non-zero univariate polynomials such that the infimum inf V(f : H) of V(f : H) is a root of some polynomial in U whenever inf V(f : H) = ±∞.The strategies of this paper are decomposing a finite set of polynomials into triangular chains of polynomials and computing the so-called revised resultants. With the aid of the computer algebraic system Maple, our algorithm has been made into a general program to treat the equality-constrained minimization of polynomials with rational coefficients.展开更多
文摘This article presents an application of generalized pattern search （PS） algorithm to solve economic load dispatch （ELD） problems with convex and non-convex fuel cost objective functions. Main objective of ELI） is to determine the most economic generating dispatch required to satisfy the predicted load demands including line losses. Relaxing various equality and inequality constraints are considered. The unit operation minhnum/maximum constraints, effects of valve-point and line losses are considered for the practical applications. Several case studies were tested and verified, which indicate an improvement in total fuel cost savings. The robustness of the proposed PS method have been assessed and investigated through intensive comparisons with reported results in recent researches. The results are very encouraging and suggesting that PS may be very useful tool in solving power system ELD problems.
基金supported by the National Basic Research Program of China under Grant No. 2006CB705500the National Natural Science Foundation of China under Grant No. 0631001+1 种基金the Program for Changjiang Scholars and Innovative Research Team in University Volvo Research and Educational Foundations
文摘By handling the travel cost function artfully, the authors formulate the transportation mixed network design problem （MNDP） as a mixed-integer, nonlinear bilevel programming problem, in which the lower-level problem, comparing with that of conventional bilevel DNDP models, is not a side constrained user equilibrium assignment problem, but a standard user equilibrium assignment problem. Then, the bilevel programming model for MNDP is reformulated as a continuous version of bilevel programming problem by the continuation method. By virtue of the optimal-value function, the lower-level assignment problem can be expressed as a nonlinear equality constraint. Therefore, the bilevel programming model for MNDP can be transformed into an equivalent single-level optimization problem. By exploring the inherent nature of the MNDP, the optimal-value function for the lower- level equilibrium assignment problem is proved to be continuously differentiable and its functional value and gradient can be obtained efficiently. Thus, a continuously differentiable but still nonconvex optimization formulation of the MNDP is created, and then a locally convergent algorithm is proposed by applying penalty function method. The inner loop of solving the subproblem is mainly to implement an Ml-or-nothing assignment. Finally, a small-scale transportation network and a large-scale network are presented to verify the proposed model and algorithm.
基金supported by the National Science Foundation of China under Grant No.10871130the Ph.D Foundation under Grant No.20093127110005+1 种基金the Shanghai Leading Academic Discipline Project under Grant No.S30405the Innovation Program of Shanghai Municipal Education Commission under Grant No.12YZ174
文摘This paper proposes a nonmonotone line search filter method with reduced Hessian updating for solving nonlinear equality constrained optimization.In order to deal with large scale problems,a reduced Hessian matrix is approximated by BFGS updates.The new method assures global convergence without using a merit function.By Lagrangian function in the filter and nonmonotone scheme,the authors prove that the method can overcome Maratos effect without using second order correction step so that the locally superlinear convergence is achieved.The primary numerical experiments are reported to show effectiveness of the proposed algorithm.
基金supported by the National Natural Science Foundation of China under Grant Nos.11271329 and 10971193
文摘The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty function with two penalty parameters for inequality constrained bilevel programming. Under some conditions, the optimal solution to the bilevel programming defined by the quadratic objective penalty function is proved to be an optimal solution to the original bilevel programming. Moreover, based on the quadratic objective penalty function, an algorithm is developed to l^nd an optimal solution to the original bilevel programming, and its convergence proved under some conditions. Furthermore, under the assumption of convexity at function without lower level problems is defined and lower level problems, a quadratic objective penalty is proved equal to the original bilevel programming.
基金the National Natural Science Special-Purpose Foundation of China （No. 10826079） the National Natural Science Foundation of China （No. 10671019） the Initial Research Fund of China Agricultural University （No. 2006061）.
文摘Let β 〉 0 and Sβ ：= {z ∈ C ： ｜Imz｜ 〈β} be a strip in the complex plane. For an integer r ≥ 0, let H∞^Г,β denote those real-valued functions f on R, which are analytic in Sβ and satisfy the restriction ｜f^（r）（z）｜ ≤ 1, z ∈ Sβ. For σ 〉 0, denote by Bσ the class of functions f which have spectra in （-2πσ, 2πσ）. And let Bσ^⊥ be the class of functions f which have no spectrum in （-2πσ, 2πσ）. We prove an inequality of Bohr type‖f‖∞≤π/√λ∧σ^r∑k=0^∞（-1）^k（r＋1）/（2k＋1）^rsinh（（2k＋1）2σβ）,f∈H∞^r,β∩B1/σ,where λ∈（0,1）,∧and ∧′are the complete elliptic integrals of the first kind for the moduli λ and λ′=√1- λ^2,respectively,and λ satisfies4∧β/π∧′=1/σ.The constant in the above inequality is exact.
基金supported by National Natural Science Foundation of China(Grant No.11161034)
文摘This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,..., xn] and a finite subset H of R[x1,..., xn], denote by V(f : H) the set {f( ˉα) | ˉα∈ Rn, and h( ˉα) =0, ? h ∈ H}. We provide an effective algorithm for computing a finite set U of non-zero univariate polynomials such that the infimum inf V(f : H) of V(f : H) is a root of some polynomial in U whenever inf V(f : H) = ±∞.The strategies of this paper are decomposing a finite set of polynomials into triangular chains of polynomials and computing the so-called revised resultants. With the aid of the computer algebraic system Maple, our algorithm has been made into a general program to treat the equality-constrained minimization of polynomials with rational coefficients.
