Abstract In this paper,a quasidifferentiable programming problem with inequality constraints is considered.First,a general form of optimality conditions for this problem is given,which contains the results of Luderer,...Abstract In this paper,a quasidifferentiable programming problem with inequality constraints is considered.First,a general form of optimality conditions for this problem is given,which contains the results of Luderer,Kuntz and Scholtes.Next,a new generalized K T condition is derived.The new optimality condition doesnt use Luderers regularity assumption and its Lagrangian multipliers dont depend on the particular elements in the superdifferentials of the object function and constraint functions.Finally,a penalty function for the problem is studied.Sufficient conditions of the penalty function attaining a global minimum are obtained.展开更多
The paper is concerned with the filled functions for global optimization of a continuous function of several variables.More general forms of filled functions are presented for smooth and nonsmooth optimizations.These ...The paper is concerned with the filled functions for global optimization of a continuous function of several variables.More general forms of filled functions are presented for smooth and nonsmooth optimizations.These functions have either two adjustable parameters or one adjustable parameter.Conditions on functions and on the values of parameters are given so that the constructed functions are desired filled functions.展开更多
By using Fukushima's differentiable merit function,Taji,Fukushima and Ibaraki have given a globally convergent modified Newton method for the strongly monotone variational inequality problem and proved their metho...By using Fukushima's differentiable merit function,Taji,Fukushima and Ibaraki have given a globally convergent modified Newton method for the strongly monotone variational inequality problem and proved their method to be quadratically convergent under certain assumptions in 1993.In this paper a hybrid method for the variational inequality problem under the assumptions that the mapping F is continuously differentiable and its Jacobian matrix Δ F(x) is positive definite for all x∈S rather than strongly monotone and that the set S is nonempty,polyhedral,closed and convex is proposed.Armijo type line search and trust region strategies as well as Fukushima's differentiable merit function are incorporated into the method.It is then shown that the method is well defined and globally convergent and that,under the same assumptions as those of Taji et al.,the method reduces to the basic Newton method and hence the rate of convergence is quadratic.Computational experiences show the efficiency of the proposed method.展开更多
Using the GARCH model to describe the risky asset's return process so thatits time-varying moments and conditional heteroskedasticity can be properly reflected,general multiperiod optimal investment and consumptio...Using the GARCH model to describe the risky asset's return process so thatits time-varying moments and conditional heteroskedasticity can be properly reflected,general multiperiod optimal investment and consumption problems with both fixed andproportional transactions costs are investigated in this paper. We model this kind ofdifficult problems as a dynamic stochastic optimization problem, which can cope withdifferent utility functions and any number of time periods. The procedure to solve theresulting complex nonlinear stochastic optimization problem is discussed in detail and abranch-decomposition algorithm is devised.展开更多
文摘Abstract In this paper,a quasidifferentiable programming problem with inequality constraints is considered.First,a general form of optimality conditions for this problem is given,which contains the results of Luderer,Kuntz and Scholtes.Next,a new generalized K T condition is derived.The new optimality condition doesnt use Luderers regularity assumption and its Lagrangian multipliers dont depend on the particular elements in the superdifferentials of the object function and constraint functions.Finally,a penalty function for the problem is studied.Sufficient conditions of the penalty function attaining a global minimum are obtained.
文摘The paper is concerned with the filled functions for global optimization of a continuous function of several variables.More general forms of filled functions are presented for smooth and nonsmooth optimizations.These functions have either two adjustable parameters or one adjustable parameter.Conditions on functions and on the values of parameters are given so that the constructed functions are desired filled functions.
基金Project supported by the National Natural Science Foundation of China (1 9971 0 65)
文摘By using Fukushima's differentiable merit function,Taji,Fukushima and Ibaraki have given a globally convergent modified Newton method for the strongly monotone variational inequality problem and proved their method to be quadratically convergent under certain assumptions in 1993.In this paper a hybrid method for the variational inequality problem under the assumptions that the mapping F is continuously differentiable and its Jacobian matrix Δ F(x) is positive definite for all x∈S rather than strongly monotone and that the set S is nonempty,polyhedral,closed and convex is proposed.Armijo type line search and trust region strategies as well as Fukushima's differentiable merit function are incorporated into the method.It is then shown that the method is well defined and globally convergent and that,under the same assumptions as those of Taji et al.,the method reduces to the basic Newton method and hence the rate of convergence is quadratic.Computational experiences show the efficiency of the proposed method.
基金This research is partially supported by the Natural Science Foundation of Shaanxi Province,China(2001SL09)
文摘Using the GARCH model to describe the risky asset's return process so thatits time-varying moments and conditional heteroskedasticity can be properly reflected,general multiperiod optimal investment and consumption problems with both fixed andproportional transactions costs are investigated in this paper. We model this kind ofdifficult problems as a dynamic stochastic optimization problem, which can cope withdifferent utility functions and any number of time periods. The procedure to solve theresulting complex nonlinear stochastic optimization problem is discussed in detail and abranch-decomposition algorithm is devised.
