In [1] the unconstrained minimization problem was considered and presented an algorithm without derivative. But the terminative conditions and convergence proof of the algorithm were not given. In this paper, we prese...In [1] the unconstrained minimization problem was considered and presented an algorithm without derivative. But the terminative conditions and convergence proof of the algorithm were not given. In this paper, we present a revised algorithm and prove its convergence.展开更多
Convergence properties of a class of multi-directional parallel quasi-Newton algorithms for the solution of unconstrained minimization problems are studied in this paper. At each iteration these algorithms generate se...Convergence properties of a class of multi-directional parallel quasi-Newton algorithms for the solution of unconstrained minimization problems are studied in this paper. At each iteration these algorithms generate several different quasi-Newton directions, and then apply line searches to determine step lengths along each direction, simultaneously. The next iterate is obtained among these trail points by choosing the lowest point in the sense of function reductions. Different quasi-Newton updating formulas from the Broyden family are used to generate a main sequence of Hessian matrix approximations. Based on the BFGS and the modified BFGS updating formulas, the global and superlinear convergence results are proved. It is observed that all the quasi-Newton directions asymptotically approach the Newton direction in both direction and length when the iterate sequence converges to a local minimum of the objective function, and hence the result of superlinear convergence follows.展开更多
The step-size procedure is very important for solving optimization problems. The Armijo step-size rule, the Armijo-Goldstein step-size rule and the Wolfe-Powell step-size rule are three well-known line search methods....The step-size procedure is very important for solving optimization problems. The Armijo step-size rule, the Armijo-Goldstein step-size rule and the Wolfe-Powell step-size rule are three well-known line search methods. On the basis of the above three types of line search methods and the idea of the proximal point methods, a new class of step-size rules was proposed. Instead of a single objective function f, f ＋1/2（x - xk）^TBk（x-Xk） was used as the merit function in iteration k, where Sk is a given symmetric positive definite matrix. The existence of the steplength for the new rules was proved. Some convergence properties were also discussed.展开更多
In this paper, we propose an extended Levenberg-Marquardt （ELM） framework that generalizes the classic Levenberg-Marquardt （LM） method to solve the unconstrained minimization problem min ρ（r（x））, where r ： R...In this paper, we propose an extended Levenberg-Marquardt （ELM） framework that generalizes the classic Levenberg-Marquardt （LM） method to solve the unconstrained minimization problem min ρ（r（x））, where r ： Rn→ Rm and ρ ： Rm → R. We also develop a few inexact variants which generalize ELM to the cases where the inner subproblem is not solved exactly and the Jaeobian is simplified, or perturbed. Global convergence and local superlinear convergence are established under certain suitable conditions. Numerical results show that our methods are promising.展开更多
Based on a class of functions, which generalize the squared Fischer-Burmeister NCP function and have many desirable properties as the latter function has, we reformulate nonlinear complementarity problem (NCP for shor...Based on a class of functions, which generalize the squared Fischer-Burmeister NCP function and have many desirable properties as the latter function has, we reformulate nonlinear complementarity problem (NCP for short) as an equivalent unconstrained optimization problem, for which we propose a derivative-free de- scent method in monotone case. We show its global convergence under some mild conditions. If F, the function involved in NCP, is Ro-function, the optimization problem has bounded level sets. A local property of the merit function is discussed. Finally, we report some numerical results.展开更多
This study aimed to develop an approach for the understanding of the relationship between the contact interaction properties of lugs and their strength and mass to design efficient and lightweight lugs for aerospace c...This study aimed to develop an approach for the understanding of the relationship between the contact interaction properties of lugs and their strength and mass to design efficient and lightweight lugs for aerospace components.Lugs are crucial components of many aerospace mechanisms,and their properties are closely linked to their contact interactions with bushings.The approach taken in this study involved modeling the adhesive layer between the lug and bushing and optimizing the dimensions of the polymer lug and metal bushing to minimize the lug’s mass while maintaining adequate strength.Finite element analysis(FEA)and cohesive zone modeling(CZM)were used to simulate the effects of primary properties of contact interaction between lug body and bushing on the strength and mass of the lug,and both gradient-free and gradient-based optimization algorithms were employed to minimize the lug’s mass while maintaining its strength.The results showed that increasing shear and tensile contact strengths reduced the resulting mass,with tangential stress having the greatest effect.Moreover,increasing contact strength reduced the required dimensions of the lug and bushing,indicating the possibility of reducing the mass of the bushing–lug assembly using rougher bushings or ribbing.展开更多
文摘In [1] the unconstrained minimization problem was considered and presented an algorithm without derivative. But the terminative conditions and convergence proof of the algorithm were not given. In this paper, we present a revised algorithm and prove its convergence.
基金This work is supported by National Science Foundation of China： 10231060.
文摘Convergence properties of a class of multi-directional parallel quasi-Newton algorithms for the solution of unconstrained minimization problems are studied in this paper. At each iteration these algorithms generate several different quasi-Newton directions, and then apply line searches to determine step lengths along each direction, simultaneously. The next iterate is obtained among these trail points by choosing the lowest point in the sense of function reductions. Different quasi-Newton updating formulas from the Broyden family are used to generate a main sequence of Hessian matrix approximations. Based on the BFGS and the modified BFGS updating formulas, the global and superlinear convergence results are proved. It is observed that all the quasi-Newton directions asymptotically approach the Newton direction in both direction and length when the iterate sequence converges to a local minimum of the objective function, and hence the result of superlinear convergence follows.
基金Project supported by the National Natural Science Foundation of China（Grant No.10161002）, and the Natural Science Foundation of Guangxi Province （Grant No.0135004）
文摘The step-size procedure is very important for solving optimization problems. The Armijo step-size rule, the Armijo-Goldstein step-size rule and the Wolfe-Powell step-size rule are three well-known line search methods. On the basis of the above three types of line search methods and the idea of the proximal point methods, a new class of step-size rules was proposed. Instead of a single objective function f, f ＋1/2（x - xk）^TBk（x-Xk） was used as the merit function in iteration k, where Sk is a given symmetric positive definite matrix. The existence of the steplength for the new rules was proved. Some convergence properties were also discussed.
文摘In this paper, we propose an extended Levenberg-Marquardt （ELM） framework that generalizes the classic Levenberg-Marquardt （LM） method to solve the unconstrained minimization problem min ρ（r（x））, where r ： Rn→ Rm and ρ ： Rm → R. We also develop a few inexact variants which generalize ELM to the cases where the inner subproblem is not solved exactly and the Jaeobian is simplified, or perturbed. Global convergence and local superlinear convergence are established under certain suitable conditions. Numerical results show that our methods are promising.
基金the National Natural Science Foundation of China
文摘Based on a class of functions, which generalize the squared Fischer-Burmeister NCP function and have many desirable properties as the latter function has, we reformulate nonlinear complementarity problem (NCP for short) as an equivalent unconstrained optimization problem, for which we propose a derivative-free de- scent method in monotone case. We show its global convergence under some mild conditions. If F, the function involved in NCP, is Ro-function, the optimization problem has bounded level sets. A local property of the merit function is discussed. Finally, we report some numerical results.
基金financially supported by the Russian Science Foundation,project no.22-79-10309.
文摘This study aimed to develop an approach for the understanding of the relationship between the contact interaction properties of lugs and their strength and mass to design efficient and lightweight lugs for aerospace components.Lugs are crucial components of many aerospace mechanisms,and their properties are closely linked to their contact interactions with bushings.The approach taken in this study involved modeling the adhesive layer between the lug and bushing and optimizing the dimensions of the polymer lug and metal bushing to minimize the lug’s mass while maintaining adequate strength.Finite element analysis(FEA)and cohesive zone modeling(CZM)were used to simulate the effects of primary properties of contact interaction between lug body and bushing on the strength and mass of the lug,and both gradient-free and gradient-based optimization algorithms were employed to minimize the lug’s mass while maintaining its strength.The results showed that increasing shear and tensile contact strengths reduced the resulting mass,with tangential stress having the greatest effect.Moreover,increasing contact strength reduced the required dimensions of the lug and bushing,indicating the possibility of reducing the mass of the bushing–lug assembly using rougher bushings or ribbing.
