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1.
Several nonlinear Lagrangian formulations have been recently proposed for
bounded integer programming problems. While possessing an asymptotic strong duality
property, these formulations offer a success guarantee for the identification of an optimal
primal solution via a dual search. Investigating common features of nonlinear Lagrangian
formulations in constructing a nonlinear support for nonconvex piecewise constant perturbation function, this paper proposes
a generalized nonlinear Lagrangian formulation of which many existing nonlinear Lagrangian formulations become special cases. 相似文献
2.
An Interior-Point Algorithm for Nonconvex Nonlinear Programming 总被引:11,自引:0,他引:11
Robert J. Vanderbei David F. Shanno 《Computational Optimization and Applications》1999,13(1-3):231-252
The paper describes an interior-point algorithm for nonconvex nonlinear programming which is a direct extension of interior-point methods for linear and quadratic programming. Major modifications include a merit function and an altered search direction to ensure that a descent direction for the merit function is obtained. Preliminary numerical testing indicates that the method is robust. Further, numerical comparisons with MINOS and LANCELOT show that the method is efficient, and has the promise of greatly reducing solution times on at least some classes of models. 相似文献
3.
Interior-Point Algorithms for Semidefinite Programming Based on a Nonlinear Formulation 总被引:2,自引:0,他引:2
Samuel Burer Renato D.C. Monteiro Yin Zhang 《Computational Optimization and Applications》2002,22(1):49-79
Recently in Burer et al. (Mathematical Programming A, submitted), the authors of this paper introduced a nonlinear transformation to convert the positive definiteness constraint on an n × n matrix-valued function of a certain form into the positivity constraint on n scalar variables while keeping the number of variables unchanged. Based on this transformation, they proposed a first-order interior-point algorithm for solving a special class of linear semidefinite programs. In this paper, we extend this approach and apply the transformation to general linear semidefinite programs, producing nonlinear programs that have not only the n positivity constraints, but also n additional nonlinear inequality constraints. Despite this complication, the transformed problems still retain most of the desirable properties. We propose first-order and second-order interior-point algorithms for this type of nonlinear program and establish their global convergence. Computational results demonstrating the effectiveness of the first-order method are also presented. 相似文献
4.
In this paper, we conduct three case studies to assess the effectiveness of a recently proposed first-order method for robust
nonlinear programming [Zhang, Y.: J. Optim. Theory Appl. 132, 111–124 (2007)]. Three robust nonlinear programming problems were chosen from the literature using the criteria that results calculated
using other methods must be available and the problems should be realistic, but fairly simple. Our studies show that the first-order
method produced reasonable solutions when the level of uncertainty was small to moderate. In addition, we demonstrate a method
for leveraging a theoretical result to eliminate constraint violations. Since the first-order method is relatively inexpensive
in comparison to other robust optimization techniques, our studies indicate that, under moderate uncertainty, the first-order
approach may be more suitable than other methods for large problems.
The authors recognize funding from NSF Grants DMS-0405831 and DMS-0240058. 相似文献
5.
6.
灰色非线性约束规划是灰色系统中一个重要的优化问题.为求解灰色非线性约束规划,给出了一种改进引力搜索算法的求解方法.实验结果表明改进引力搜索算法对求解灰色非线性约束规划可行有效. 相似文献
7.
Global Optimization of Nonlinear Bilevel Programming Problems 总被引:5,自引:0,他引:5
A novel technique that addresses the solution of the general nonlinear bilevel programming problem to global optimality is presented. Global optimality is guaranteed for problems that involve twice differentiable nonlinear functions as long as the linear independence constraint qualification condition holds for the inner problem constraints. The approach is based on the relaxation of the feasible region by convex underestimation, embedded in a branch and bound framework utilizing the basic principles of the deterministic global optimization algorithm, BB [2, 4, 5, 11]. Epsilon global optimality in a finite number of iterations is theoretically guaranteed. Computational studies on several literature problems are reported. 相似文献
8.
We introduce a discrete penalty called Boolean Penalty to 0–1 constrained nonlinear programming (PNLC-01). The main importance of this Penalty function are its properties which allow us to develop algorithms for the PNLC-01 problem. Optimality conditions, and numerical results are presented. 相似文献
9.
对非线性规划问题的处理通常采用罚函数法,使用罚函数法的困难在于参数的选取.本文提出了一种解非线性规划问题非参数罚函数多目标正交遗传算法,对违反约束的个体进行动态的惩罚以保持群体中不可行解的一定比例,从而不但有效增加种群的多样性,而且避免了传统的过度惩罚缺陷,使群体更好地向最优解逼近.数据实验表明该算法对带约束的非线性规划问题求解是非常有效的. 相似文献
10.
Interior-Point Methods for Nonconvex Nonlinear Programming: Filter Methods and Merit Functions 总被引:2,自引:0,他引:2
Hande Y. Benson Robert J. Vanderbei David F. Shanno 《Computational Optimization and Applications》2002,23(2):257-272
Recently, Fletcher and Leyffer proposed using filter methods instead of a merit function to control steplengths in a sequential quadratic programming algorithm. In this paper, we analyze possible ways to implement a filter-based approach in an interior-point algorithm. Extensive numerical testing shows that such an approach is more efficient than using a merit function alone. 相似文献
11.
针对非线性0-1规划,提出采用一种智能优化算法——蜂群算法进行求解.描述了蜂群算法的实现过程,并在计算机上编程予以实现.经大量实例测试,并与其它算法进行比较,获得了满意的结果.说明了蜂群算法在解决非线性0-1规划问题上的可行性与有效性,同时具有良好的优化能力.. 相似文献
12.
Sven Leyffer 《Computational Optimization and Applications》2001,18(3):295-309
This paper considers the solution of Mixed Integer Nonlinear Programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving Nonlinear Programming (NLP) and Mixed Integer Linear Programming problems.In contrast, an integrated approach to solving MINLP problems is considered here. This new algorithm is based on branch-and-bound, but does not require the NLP problem at each node to be solved to optimality. Instead, branching is allowed after each iteration of the NLP solver. In this way, the nonlinear part of the MINLP problem is solved whilst searching the tree. The nonlinear solver that is considered in this paper is a Sequential Quadratic Programming solver.A numerical comparison of the new method with nonlinear branch-and-bound is presented and a factor of up to 3 improvement over branch-and-bound is observed. 相似文献
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14.
A Simple Primal-Dual Feasible Interior-Point Method for Nonlinear Programming with Monotone Descent 总被引:1,自引:0,他引:1
We propose and analyze a primal-dual interior point method of the feasible type, with the additional property that the objective function decreases at each iteration. A distinctive feature of the method is the use of different barrier parameter values for each constraint, with the purpose of better steering the constructed sequence away from non-KKT stationary points. Assets of the proposed scheme include relative simplicity of the algorithm and of the convergence analysis, strong global and local convergence properties, and good performance in preliminary tests. In addition, the initial point is allowed to lie on the boundary of the feasible set. 相似文献
15.
Nonlinear Proximal Decomposition Method for Convex Programming 总被引:2,自引:0,他引:2
In this paper, we propose a new decomposition method for solving convex programming problems with separable structure. The proposed method is based on the decomposition method proposed by Chen and Teboulle and the nonlinear proximal point algorithm using the Bregman function. An advantage of the proposed method is that, by a suitable choice of the Bregman function, each subproblem becomes essentially the unconstrained minimization of a finite-valued convex function. Under appropriate assumptions, the method is globally convergent to a solution of the problem. 相似文献
16.
J.L. Alejandre Ana Allueva Jose Miguel Gonzalez 《Computational Optimization and Applications》2004,27(1):83-93
The degree of difficulty is an important concept in classical geometric programming theory. The dual problem is often infeasible when the degree of difficulty is negative and little has been published on this topic. In this paper, an alternative procedure is developed to find the optimal solution for the posynomial geometric programming problem with a negative degree of difficulty. First an equivalent problem was constructed with a positive degree of difficulty and the general posynomial geometric programming problem was solved using an original method previously developed by the authors. This method avoids the difficulty of non-differentiability of the dual objective function in the classical methods classified as dual. It also avoids the problem that appears when the feasible region for the dual problem is formed by an inconsistent system of linear equations. 相似文献
17.
El-Alem M. M. El-Sayed S. El-Sobky B. 《Journal of Optimization Theory and Applications》2004,120(3):487-502
In this paper, a formulation for an interior-point Newton method of general nonlinear programming problems is presented. The formulation uses the Coleman-Li scaling matrix. The local convergence and the q-quadratic rate of convergence for the method are established under the standard assumptions of the Newton method for general nonlinear programming. 相似文献
18.
In recent work, the local convergence behavior of path-following interior-point methods and sequential quadratic programming methods for nonlinear programming has been investigated for the case in which the assumption of linear independence of the active constraint gradients at the solution is replaced by the weaker Mangasarian–Fromovitz constraint qualification. In this paper, we describe a stabilization of the primal-dual interior-point approach that ensures rapid local convergence under these conditions without enforcing the usual centrality condition associated with path-following methods. The stabilization takes the form of perturbations to the coefficient matrix in the step equations that vanish as the iterates converge to the solution. 相似文献
19.
多约束非线性整数规划是一类非常重要的问题,非线性背包问题是它的一类特殊而重要的问题.定义在有限整数集上极大化一个可分离非线性函数的多约束最优化问题.这类问题常常用于资源分配、工业生产及计算机网络的最优化模型中,运用一种新的割平面法来求解对偶问题以得到上界,不仅减少了对偶间隙,而且保证了算法的收敛性.利用区域割丢掉某些整数箱子,并把剩下的区域划分为一些整数箱子的并集,以便使拉格朗日松弛问题能有效求解,且使算法在有限步内收敛到最优解.算法把改进的割平面法用于求解对偶问题并与区域分割有效结合解决了多约束非线性背包问题的求解.数值结果表明了改进的割平面方法对对偶搜索更加有效. 相似文献