The self-scaling quasi-Newton method solves an unconstrained optimization problem by scaling the Hessian approximation matrix before it is updated at each iteration to avoid the possible large eigenvalues in the Hessi...The self-scaling quasi-Newton method solves an unconstrained optimization problem by scaling the Hessian approximation matrix before it is updated at each iteration to avoid the possible large eigenvalues in the Hessian approximation matrices of the objective function. It has been proved in the literature that this method has the global and superlinear convergence when the objective function is convex （or even uniformly convex）. We propose to solve unconstrained nonconvex optimization problems by a self-scaling BFGS algorithm with nonmonotone linear search. Nonmonotone line search has been recognized in numerical practices as a competitive approach for solving large-scale nonlinear problems. We consider two different nonmonotone line search forms and study the global convergence of these nonmonotone self-scale BFGS algorithms. We prove that, under some weaker condition than that in the literature, both forms of the self-scaling BFGS algorithm are globally convergent for unconstrained nonconvex optimization problems.展开更多
China is experienciug from serious water issues. There are many differences among the Nine Major Rivers basins of China in the construction of dikes, reservoirs, floodgates, flood discharge projects, flood diversion p...China is experienciug from serious water issues. There are many differences among the Nine Major Rivers basins of China in the construction of dikes, reservoirs, floodgates, flood discharge projects, flood diversion projects, water ecological constructions, water conservancy management, etc. The shadow prices of water resources for Nine Major Rivers can provide suggestions to the Chinese goverument. This article develops a dynamic shadow prices approach based on a multipeziod input-output optimizing model. Unlike previous approaches, the new model is based on the dynamic computable general equilibrium （DCGE） model to solve the problem of marginal long-term prices of water resources. First, definitions and algorithms of DCGE are elaborated. Second, the results of shadow prices of water resources for Nine Major Rivers in 1949-2050 in China using the National Water Conservancy input-holdiug-out in table for Nine Major Rivers in 1999 are listed. A conclusion of this article is that the shadow prices of water resources for Nine Major Rivers are largely based on the extent of scarcity. Selling prices of water resources should be revised via the usage of parameters representing shadow prices.展开更多
基金supported by NSFC 10001031 and 70472074supported by NSERC Grant 283103
文摘The self-scaling quasi-Newton method solves an unconstrained optimization problem by scaling the Hessian approximation matrix before it is updated at each iteration to avoid the possible large eigenvalues in the Hessian approximation matrices of the objective function. It has been proved in the literature that this method has the global and superlinear convergence when the objective function is convex （or even uniformly convex）. We propose to solve unconstrained nonconvex optimization problems by a self-scaling BFGS algorithm with nonmonotone linear search. Nonmonotone line search has been recognized in numerical practices as a competitive approach for solving large-scale nonlinear problems. We consider two different nonmonotone line search forms and study the global convergence of these nonmonotone self-scale BFGS algorithms. We prove that, under some weaker condition than that in the literature, both forms of the self-scaling BFGS algorithm are globally convergent for unconstrained nonconvex optimization problems.
基金National Nature Science Foundation of China(No.70472074.No.70131002.and No.60474063)China Postdoctoral Science Foundation.
文摘China is experienciug from serious water issues. There are many differences among the Nine Major Rivers basins of China in the construction of dikes, reservoirs, floodgates, flood discharge projects, flood diversion projects, water ecological constructions, water conservancy management, etc. The shadow prices of water resources for Nine Major Rivers can provide suggestions to the Chinese goverument. This article develops a dynamic shadow prices approach based on a multipeziod input-output optimizing model. Unlike previous approaches, the new model is based on the dynamic computable general equilibrium （DCGE） model to solve the problem of marginal long-term prices of water resources. First, definitions and algorithms of DCGE are elaborated. Second, the results of shadow prices of water resources for Nine Major Rivers in 1949-2050 in China using the National Water Conservancy input-holdiug-out in table for Nine Major Rivers in 1999 are listed. A conclusion of this article is that the shadow prices of water resources for Nine Major Rivers are largely based on the extent of scarcity. Selling prices of water resources should be revised via the usage of parameters representing shadow prices.
