In present paper, a modified maximum entropy method is proposed to solve minimax problem. This method is a generalization of well-known called maximum entropy method and attempts to overcome some drawbacks of former m...In present paper, a modified maximum entropy method is proposed to solve minimax problem. This method is a generalization of well-known called maximum entropy method and attempts to overcome some drawbacks of former method. Some properties of new approximate function are presented first and then several numerical examples are given according to modified algorithm, which illustrates that our method is superior to former one.展开更多
A nonlinear minimax problem is usually defined aswherefi(x), i=1,…,m, are generally smooth nonlinear functions of a vector x ∈ R^n. Since the objective φ(x) is a non-smooth function, (A) is then a non-smooth, uncon...A nonlinear minimax problem is usually defined aswherefi(x), i=1,…,m, are generally smooth nonlinear functions of a vector x ∈ R^n. Since the objective φ(x) is a non-smooth function, (A) is then a non-smooth, unconstrained optimization problem and cannot be solved by standard unconstrained minimization algorithms. One normally transforms it into an equivalent nonlinear programming problem:展开更多
In this paper, we propose a modified trust-region filter method algorithm for Minimax problems, which based on the framework of SQP-filter method and associated with the technique of nonmonotone method. We use the SQP...In this paper, we propose a modified trust-region filter method algorithm for Minimax problems, which based on the framework of SQP-filter method and associated with the technique of nonmonotone method. We use the SQP subproblem to acquire an attempt step, and use the filter to weigh the effect of the attempt step so as to avoid using penalty function. The algorithm uses the Lagrange function as a merit function and the nonmonotone filter to improve the effect of the algorithm. Under some mild conditions, we prove the global convergence.展开更多
In non-smooth optimization,one particular problem which often appears inengineering designs,electrical engineering and game theory is called nonlinear minimaxproblem.For the non-smooth properties of objective function...In non-smooth optimization,one particular problem which often appears inengineering designs,electrical engineering and game theory is called nonlinear minimaxproblem.For the non-smooth properties of objective functions,there are some difficultiesin solving this problem.Since 1987,taking into account the entropy funtions,experts havehad several excellent results such as refs.[1—5].However,those methods are limited展开更多
To solve the inequality problem, an adjustable entropy method is proposed. An inequality problem can be transformed into a minimax problem which is nondifferentiable; then an adjustable entropy is used to smooth the m...To solve the inequality problem, an adjustable entropy method is proposed. An inequality problem can be transformed into a minimax problem which is nondifferentiable; then an adjustable entropy is used to smooth the minimax problem. The solution of inequalities can be approached by using a BFGS algorithm of the standard optimization method. Some properties of the new approximate function are presented and then the global convergence are given according to the algorithm. Two numerical examples illustrate that the proposed method is efficient and is superior to the former ones.展开更多
文摘In present paper, a modified maximum entropy method is proposed to solve minimax problem. This method is a generalization of well-known called maximum entropy method and attempts to overcome some drawbacks of former method. Some properties of new approximate function are presented first and then several numerical examples are given according to modified algorithm, which illustrates that our method is superior to former one.
基金Project supported by the National Natural Science Foundation of China
文摘A nonlinear minimax problem is usually defined aswherefi(x), i=1,…,m, are generally smooth nonlinear functions of a vector x ∈ R^n. Since the objective φ(x) is a non-smooth function, (A) is then a non-smooth, unconstrained optimization problem and cannot be solved by standard unconstrained minimization algorithms. One normally transforms it into an equivalent nonlinear programming problem:
文摘In this paper, we propose a modified trust-region filter method algorithm for Minimax problems, which based on the framework of SQP-filter method and associated with the technique of nonmonotone method. We use the SQP subproblem to acquire an attempt step, and use the filter to weigh the effect of the attempt step so as to avoid using penalty function. The algorithm uses the Lagrange function as a merit function and the nonmonotone filter to improve the effect of the algorithm. Under some mild conditions, we prove the global convergence.
基金Project supported by the National Natural Science Foundation of China.
文摘In non-smooth optimization,one particular problem which often appears inengineering designs,electrical engineering and game theory is called nonlinear minimaxproblem.For the non-smooth properties of objective functions,there are some difficultiesin solving this problem.Since 1987,taking into account the entropy funtions,experts havehad several excellent results such as refs.[1—5].However,those methods are limited
文摘To solve the inequality problem, an adjustable entropy method is proposed. An inequality problem can be transformed into a minimax problem which is nondifferentiable; then an adjustable entropy is used to smooth the minimax problem. The solution of inequalities can be approached by using a BFGS algorithm of the standard optimization method. Some properties of the new approximate function are presented and then the global convergence are given according to the algorithm. Two numerical examples illustrate that the proposed method is efficient and is superior to the former ones.
