A level-value estimation method was illustrated for solving the constrained global optimization problem. The equivalence between the root of a modified variance equation and the optimal value of the original optimizat...A level-value estimation method was illustrated for solving the constrained global optimization problem. The equivalence between the root of a modified variance equation and the optimal value of the original optimization problem is shown. An alternate algorithm based on the Newton＇s method is presented and the convergence of its implementable approach is proved. Preliminary numerical results indicate that the method is effective.展开更多
The penalty method is a popular method for solving constrained optimization problems, which can change the constrained optimization to the unconstrained optimization. With the integral-level set method, a new approach...The penalty method is a popular method for solving constrained optimization problems, which can change the constrained optimization to the unconstrained optimization. With the integral-level set method, a new approach was proposed, which is briefer than the penalty method, to achieve the transform by constructing a simple function, then a level-value function was introduced to construct the equivalence between the unconstrained optimization and a nonlinear equality. By studying the properties of the function, a level-value estimate algorithm and an implementation algorithm were given by means of the uniform distribution of the good point set. Key words global optimization - constrained optimization - integral-level set - level-value estimate MSC 2000 90C05展开更多
In this paper,we propose a stochastic level-value estimation method to solve a kind of box-constrained global optimization problem.For this purpose,we first derive a generalized variance function associated with the c...In this paper,we propose a stochastic level-value estimation method to solve a kind of box-constrained global optimization problem.For this purpose,we first derive a generalized variance function associated with the considered problem and prove that the largest root of the function is the global minimal value.Then,Newton’s method is applied to find the root.The convergence of the proposed method is established under some suitable conditions.Based on the main idea of the cross-entropy method to update the sampling density function,an important sampling technique is proposed in the implementation.Preliminary numerical experiments indicate the validity of the proposed method.展开更多
基金Project supported by the National Natural Science Foundation of China (No.19871053)
文摘A level-value estimation method was illustrated for solving the constrained global optimization problem. The equivalence between the root of a modified variance equation and the optimal value of the original optimization problem is shown. An alternate algorithm based on the Newton＇s method is presented and the convergence of its implementable approach is proved. Preliminary numerical results indicate that the method is effective.
文摘The penalty method is a popular method for solving constrained optimization problems, which can change the constrained optimization to the unconstrained optimization. With the integral-level set method, a new approach was proposed, which is briefer than the penalty method, to achieve the transform by constructing a simple function, then a level-value function was introduced to construct the equivalence between the unconstrained optimization and a nonlinear equality. By studying the properties of the function, a level-value estimate algorithm and an implementation algorithm were given by means of the uniform distribution of the good point set. Key words global optimization - constrained optimization - integral-level set - level-value estimate MSC 2000 90C05
文摘In this paper,we propose a stochastic level-value estimation method to solve a kind of box-constrained global optimization problem.For this purpose,we first derive a generalized variance function associated with the considered problem and prove that the largest root of the function is the global minimal value.Then,Newton’s method is applied to find the root.The convergence of the proposed method is established under some suitable conditions.Based on the main idea of the cross-entropy method to update the sampling density function,an important sampling technique is proposed in the implementation.Preliminary numerical experiments indicate the validity of the proposed method.
