generalized geometric programming (GGP) problems consist of a signomial being minimized in the objective function subject to signomial constraints, and such problems have been utilized in various fields. After modelin...
详细信息
generalized geometric programming (GGP) problems consist of a signomial being minimized in the objective function subject to signomial constraints, and such problems have been utilized in various fields. After modeling numerous applications as GGP problems, solving them has become a significant requirement. A convex underestimator is considered an important concept to solve GGP problems for obtaining the global minimum. Among convex underestimators, variable transformation is one of the most popular techniques. This study utilizes an estimator to solve the difficulty of selecting an appropriate transformation between the exponential transformation and power convex transformation techniques and considers all popular types of transformation techniques to develop a novel and efficient convexification strategy for solving GGP problems. This proposed convexification strategy offers a guide for selecting the most appropriate transformation techniques on any condition of a signomial term to obtain the tightest convex underestimator. Several numerical examples in the online supplement are presented to investigate the effects of different convexification strategies on GGP problems and demonstrate the effectiveness of the proposed convexification strategy with regard to both solution quality and computation efficiency.
generalized geometric programming (GGP) problems are converted to mixed-integer linear programming (MILP) problems using piecewise-linear approximations. Our approach is to approximate a multiple-term log-sum function...
详细信息
generalized geometric programming (GGP) problems are converted to mixed-integer linear programming (MILP) problems using piecewise-linear approximations. Our approach is to approximate a multiple-term log-sum function of the form log(x(1) + x(2) + ... +x(n)) in terms of a set of linear equalities or inequalities of logx(1), logx(2), ... , and logx(n), where x(1,) ... , x(n), are strictly positive. The advantage of this approach is its simplicity and readiness to implement and solve using commercial MILP solvers. While MILP problems in general are no easier than GGP problems, this approach is justified by the phenomenal progress of computing power of both personal computers and commercial MILP solvers. The limitation of this approach is discussed along with numerical tests. (C) 2015 Elsevier B.V. All rights reserved.
generalized geometric programming (GGP) problems occur frequently in engineering design and management, but most existing methods for solving GGP actually only consider continuous variables. This article presents a ne...
详细信息
generalized geometric programming (GGP) problems occur frequently in engineering design and management, but most existing methods for solving GGP actually only consider continuous variables. This article presents a new branch-and-bound algorithm for globally solving GGP problems with discrete variables. For minimizing the problem, an equivalent monotonic optimization problem (P) with discrete variables is presented by exploiting the special structure of GGP. In the algorithm, the lower bounds are computed by solving ordinary linear programming problems that are derived via a linearization technique. In contrast to pure branch-and-bound methods, the algorithm can perform a domain reduction cut per iteration by using the monotonicity of problem (P), which can suppress the rapid growth of branching tree in the branch-and-bound search so that the performance of the algorithm is further improved. Computational results for several sample examples and small randomly generated problems are reported to vindicate our conclusions.
This article presents a branch-reduction-bound algorithm for globally solving the generalized geometric programming problem. To solve the problem, an equivalent monotonic optimization problem whose objective function ...
详细信息
This article presents a branch-reduction-bound algorithm for globally solving the generalized geometric programming problem. To solve the problem, an equivalent monotonic optimization problem whose objective function is just a simple univariate is proposed by exploiting the particularity of this problem. In contrast to usual branch-and-bound methods, in the algorithm the upper bound of the subproblem in each node is calculated easily by arithmetic expressions. Also, a reduction operation is introduced to reduce the growth of the branching tree during the algorithm search. The proposed algorithm is proven to be convergent and guarantees to find an approximative solution that is close to the actual optimal solution. Finally, numerical examples are given to illustrate the feasibility and efficiency of the present algorithm.
This article presents a branch-reduction-bound algorithm for globally solving the generalized geometric programming problem. To solve the problem, an equivalent monotonic optimization problem whose objective function ...
详细信息
This article presents a branch-reduction-bound algorithm for globally solving the generalized geometric programming problem. To solve the problem, an equivalent monotonic optimization problem whose objective function is just a simple univariate is proposed by exploiting the particularity of this problem. In contrast to usual branch-and-bound methods, in the algorithm the upper bound of the subproblem in each node is calculated easily by arithmetic expressions. Also, a reduction operation is introduced to reduce the growth of the branching tree during the algorithm search. The proposed algorithm is proven to be convergent and guarantees to find an approximative solution that is close to the actual optimal solution. Finally, numerical examples are given to illustrate the feasibility and efficiency of the present algorithm.
作者:
Lu, Hao-ChunFu Jen Catholic Univ
Dept Informat Management Coll Management 510 Jhongjheng Rd Sinjhuang City 242 Taipei County Taiwan
Free-sign pure discrete signomial (FPDS) terms are vital to and are frequently observed in many nonlinear programming problems, such as geometricprogramming, generalized geometric programming, and mixed-integer non-l...
详细信息
Free-sign pure discrete signomial (FPDS) terms are vital to and are frequently observed in many nonlinear programming problems, such as geometricprogramming, generalized geometric programming, and mixed-integer non-linear programming problems. In this study, all variables in the FPDS term are discrete variables. Any improvement to techniques for linearizing FPDS term contributes significantly to the solving of nonlinear programming problems;therefore, relative techniques have continually been developed. This study develops an improved exact method to linearize a FPDS term into a set of linear programs with minimal logarithmic numbers of zero-one variables and constraints. This method is tighter than current methods. Various numerical experiments demonstrate that the proposed method is significantly more efficient than current methods, especially when the problem scale is large.
In this paper,on the basis of making full use of the characteristics of unconstrained generalized geometric programming(GGP),we establish a nonmonotonic trust region algorithm via the conjugate path for solving unco...
详细信息
In this paper,on the basis of making full use of the characteristics of unconstrained generalized geometric programming(GGP),we establish a nonmonotonic trust region algorithm via the conjugate path for solving unconstrained GGP problem.A new type of condensation problem is presented,then a particular conjugate path is constructed for the problem,along which we get the approximate solution of the problem by nonmonotonic trust region algorithm,and further prove that the algorithm has global convergence and quadratic convergence properties.
This paper deals with model predictive control based on Wiener model. The nonlinear block of the considered model is represented by a polynomial relation and the model's parameters are determined using the neural ...
详细信息
ISBN:
(纸本)9781479917587
This paper deals with model predictive control based on Wiener model. The nonlinear block of the considered model is represented by a polynomial relation and the model's parameters are determined using the neural networks. A global optimization method, i.e. the generalized geometric programming method, is used to solve the nonconvex optimization control problem. The efficiency of the proposed controller is illustrated through a simulation example.
In this paper, a general algorithm for solving generalized geometric programming with nonpositive degree of difficulty is proposed. It shows that under certain assumptions the primal problem can be transformed and dec...
详细信息
In this paper, a general algorithm for solving generalized geometric programming with nonpositive degree of difficulty is proposed. It shows that under certain assumptions the primal problem can be transformed and decomposed into several subproblems which are easy to solve, and furthermore we verify that through solving these subproblems we can obtain the optimal value and solutions of the primal problem which are global solutions. At last, some examples are given to vindicate our conclusions.
This paper deals with model predictive control based on Wiener model. The nonlinear block of the considered model is represented by a polynomial relation and the model's parameters are determined using the neural ...
详细信息
ISBN:
(纸本)9781479917594
This paper deals with model predictive control based on Wiener model. The nonlinear block of the considered model is represented by a polynomial relation and the model's parameters are determined using the neural networks. A global optimization method, i.e. the generalized geometric programming method, is used to solve the nonconvex optimization control problem. The efficiency of the proposed controller is illustrated through a simulation example.
暂无评论