In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modif...In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function.Furthermore, a (α, η)-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of saddle point are given.展开更多
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
The alternating direction method of multipliers(ADMM)is a benchmark for solving convex programming problems with separable objective functions and linear constraints.In the literature it has been illustrated as an app...The alternating direction method of multipliers(ADMM)is a benchmark for solving convex programming problems with separable objective functions and linear constraints.In the literature it has been illustrated as an application of the proximal point algorithm(PPA)to the dual problem of the model under consideration.This paper shows that ADMM can also be regarded as an application of PPA to the primal model with a customized choice of the proximal parameter.This primal illustration of ADMM is thus complemental to its dual illustration in the literature.This PPA revisit on ADMM from the primal perspective also enables us to recover the generalized ADMM proposed by Eckstein and Bertsekas easily.A worst-case O(1/t)convergence rate in ergodic sense is established for a slight extension of Eckstein and Bertsekas’s generalized ADMM.展开更多
基金Supported by the National Natural Science Foundation of China(19871009)
文摘In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function.Furthermore, a (α, η)-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of saddle point are given.
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 National Natural Science Foundation of China(Grant Nos.11001124 and 91130007)the Doctoral Fund of Ministry of Eduction of China(Grant No.20110091110004)the General Research Fund from Hong Kong Research Grants Council(Grant No.HKBU 203712)
文摘The alternating direction method of multipliers(ADMM)is a benchmark for solving convex programming problems with separable objective functions and linear constraints.In the literature it has been illustrated as an application of the proximal point algorithm(PPA)to the dual problem of the model under consideration.This paper shows that ADMM can also be regarded as an application of PPA to the primal model with a customized choice of the proximal parameter.This primal illustration of ADMM is thus complemental to its dual illustration in the literature.This PPA revisit on ADMM from the primal perspective also enables us to recover the generalized ADMM proposed by Eckstein and Bertsekas easily.A worst-case O(1/t)convergence rate in ergodic sense is established for a slight extension of Eckstein and Bertsekas’s generalized ADMM.