Description:
In this paper, we propose a new global optimization approach based on the filled function method for solving box-constrained systems of nonlinear equations. The special properties of optimization problem are employed to construct a novel filled function. The objective function value can be reduced by half in each iteration of our filled function algorithm. Several numerical examples are presented to illustrate the efficiency of the present approach.
Description:
In this paper, we present a global optimization method based on the filled function method to solve systems of nonlinear equations. Formulating a system of nonlinear equation into an equivalent global optimization problem, we manage to find a solution or an appropriate solution of the system of nonlinear equations by solving the formulated global optimization problem. A novel filled function method is proposed to solve the global optimization problem. Two numerical examples are presented to illustrate the efficiency of this method.
Description:
A filled function method is presented in this paper to solve constrained nonlinear integer programming problems. It is shown that for a given non-global local minimizer, a better local minimizer can be obtained by local search staring from an improved initial point which is obtained by locally solving a box-constrained integer programming problem. Several illustrative numerical examples are reported to show the efficiency of the present method.
Description:
A filled function method is presented in this paper to solve constrained nonlinear integer programming problems. It is shown that for a given non-global local minimizer, a better local minimizer can be obtained by local search staring from an improved initial point which is obtained by locally solving a box-constrained integer programming problem. Several illustrative numerical examples are reported to show the efficiency of the present method.
Description:
In this article, we first introduce a definition of a local minimizer for the quadratic programs with {-1, 1} constraints and show that the existing necessary condition of global optimality in some recent literature is in fact the necessary and sufficient condition of local optimality under the present definition. A filled function and the corresponding filled function algorithm then are proposed to get the global minimizer of the concerned minimization problem. The existing sufficient condition of global optimality is employed to form one of the termination rules of the algorithm. Several numerical examples are reported to show the efficiency of the present method for solving quadratic programs with binary constraints.
Description:
In this paper, we propose an auxiliary function method to solve constrained systems of nonlinear equations. By introducing an auxiliary function, an unconstrained (box-constrained) optimization problem is constructed for a given constrained system of nonlinear equations. It is shown that any local minimizer of the constructed unconstrained optimization problem is an approximate solution to the given constrained system when parameters are appropriately chosen, and the precision for approximation can be preset. It is also shown that any accumulation point of the local minimizers of the constructed unconstrained optimization problems with a sequence of parameters tending to zero is a solution to the given constrained system of nonlinear equations.
Description:
A novel monotonization method is proposed for converting a non-monotone programming problem into a monotone programming problem. An equivalent monotone programming problem with only inequality constraints is obtained via this monotonization method. Then the existing convexification and concavification methods can be used to convert the monotone programming problem into an equivalent better-structured optimization problem.
Description:
In this article, we present some global optimality conditions for mixed quadratic programming problems. Our approach is based on a L-subdifferential and an associated L-normal cone. Unlike most subdifferentials, the L-subdifferential is formed by functions that are not necessarily linear functions. We derive some sufficient and necessary global optimality conditions for mixed quadratic programs with box constraints and binary constraints.
Description:
We consider the problem of solving a constrained system of nonlinear equations. After reformulating the system into an equivalent constrained global optimization problems, we construct a filled function based on a special property of the reformulated problem. A filled function method is then proposed to solve the constrained system of nonlinear equations. Some numerical examples are presented to illustrate the usefulness of the present techniques.
Description:
In this article, we investigate the exact penalty properties of a lower order penalty function under a lower order calmness conditions. It is shown that the local exact penalization of the lower order penalty function with any positive penalty parameter holds under the local lower order calmness condition. A necessary and sufficient condition for global exact penalization of the lower order penalty function is given in terms of global lower order calmness condition. Furthermore, a formula of least global exact penalty parameter for the lower order penalty function is obtained.
Description:
In this paper, we consider a class of mixed integer weakly concave programming problems (MIWCPP) consisting of minimizing a difference of a quadratic function and a convex function. A new necessary global optimality conditions for MIWCPP is presented in this paper. A new local optimization method for MIWCPP is designed based on the necessary global optimality conditions, which is different from the traditional local optimization method. A global optimization method is proposed by combining some auxiliary functions and the new local optimization method. Furthermore, numerical examples are also presented to show that the proposed global optimization method for MIWCPP is efficient.