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1.
Convergence of a smoothing algorithm for symmetric cone complementarity problems with a nonmonotone line search 总被引:1,自引:0,他引:1
In this paper, we propose a smoothing algorithm for solving the monotone symmetric cone complementarity problems (SCCP for
short) with a nonmonotone line search. We show that the nonmonotone algorithm is globally convergent under an assumption that
the solution set of the problem concerned is nonempty. Such an assumption is weaker than those given in most existing algorithms
for solving optimization problems over symmetric cones. We also prove that the solution obtained by the algorithm is a maximally
complementary solution to the monotone SCCP under some assumptions.
This work was supported by National Natural Science Foundation of China (Grant Nos. 10571134, 10671010) and Natural Science
Foundation of Tianjin (Grant No. 07JCYBJC05200) 相似文献
2.
In this paper, we present a predictor-corrector smoothing Newton method for solving nonlinear symmetric cone complementarity problems (SCCP) based on the symmetrically perturbed smoothing function. Under a mild assumption, the solution set of the problem concerned is just nonempty, we show that the proposed algorithm is globally and locally quadratic convergent. Also, the algorithm finds a maximally complementary solution to the SCCP. Numerical results for second order cone complementarity problems (SOCCP), a special case of SCCP, show that the proposed algorithm is effective. 相似文献
3.
Jingyong Tang Li Dong Liang Fang Jinchuan Zhou 《Journal of Applied Mathematics and Computing》2013,43(1-2):307-328
The symmetric cone complementarity problem (denoted by SCCP) is a broad class of optimization problems, which contains the semidefinite complementarity problem, the second-order cone complementarity problem, and the nonlinear complementarity problem. In this paper we first extend the smoothing function proposed by Huang et al. (Sci. China 44:1107–1114, 2001) for the nonlinear complementarity problem to the context of symmetric cones and show that it is coercive under suitable assumptions. Based on this smoothing function, a smoothing-type algorithm, which is a modified version of the Qi-Sun-Zhou method (Qi et al. in Math. Program. 87:1–35, 2000), is proposed for solving the SCCP. By using the theory of Euclidean Jordan algebras, we prove that the proposed algorithm is globally and locally quadratically convergent under suitable assumptions. Preliminary numerical results for some second-order cone complementarity problems are reported which indicate that the proposed algorithm is effective. 相似文献
4.
A Superlinearly Convergent SSLE Algorithm for Optimization Problems with Linear Complementarity Constraints 总被引:2,自引:0,他引:2
In this paper we study a special kind of optimization problems with linear complementarity constraints. First, by a generalized
complementarity function and perturbed technique, the discussed problem is transformed into a family of general nonlinear
optimization problems containing parameters. And then, using a special penalty function as a merit function, we establish
a sequential systems of linear equations (SSLE) algorithm. Three systems of equations solved at each iteration have the same
coefficients. Under some suitable conditions, the algorithm is proved to possess not only global convergence, but also strong
and superlinear convergence. At the end of the paper, some preliminary numerical experiments are reported. 相似文献
5.
6.
There recently has been much interest in smoothing Newton method for solving nonlinear complementarity problems. We extend
such method to symmetric cone complementarity problems (SCCP). In this paper, we first investigate a one-parametric class
of smoothing functions in the context of symmetric cones, which contains the Fischer–Burmeister smoothing function and the
CHKS smoothing function as special cases. Then we propose a smoothing Newton method for the SCCP based on the one-parametric
class of smoothing functions. For the proposed method, besides the classical step length, we provide a new step length and
the global convergence is obtained. Finally, preliminary numerical results are reported, which show the effectiveness of the
two step lengthes in the algorithm and provide efficient domains of the parameter for the complementarity problems. 相似文献
7.
本文以处理半无限最优化问题的一般技巧,将一类针对有限极小极大问题的信赖域算法推广到半无限极小极大问题。并证明了新建算法的全局收敛性和超线性收敛性。 相似文献
8.
The smoothing algorithms have been successfully applied to solve the symmetric cone complementarity problem (denoted by SCCP), which in general have the global and local superlinear/quadratic convergence if the solution set of the SCCP is nonempty and bounded. Huang, Hu and Han [Science in China Series A: Mathematics, 52: 833–848, 2009] presented a nonmonotone smoothing algorithm for solving the SCCP, whose global convergence is established by just requiring that the solution set of the SCCP is nonempty. In this paper, we propose a new nonmonotone smoothing algorithm for solving the SCCP by modifying the version of Huang-Hu-Han’s algorithm. We prove that the modified nonmonotone smoothing algorithm not only is globally convergent but also has local superlinear/quadratical convergence if the solution set of the SCCP is nonempty. This convergence result is stronger than those obtained by most smoothing-type algorithms. Finally, some numerical results are reported. 相似文献
9.
基于存档策略的多目标优化的遗传算法及其收敛性分析 总被引:1,自引:0,他引:1
设计了一种用遗传算法求解多目标优化问题的有效方法——基于存档策略的多目标优化的遗传算法,并讨论了此算法的收敛性.首先给出档案的定义,设计出基于支配关系下的带有存档策略遗传算法,并通过算例检验了算法的有效性;然后引入了两档案间的距离的概念,在此距离定义的基础上证明了算法在概率意义下是收敛的. 相似文献
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11.
Ahmed Roubi 《Computational Optimization and Applications》1994,3(3):259-280
We consider a method of centers for solving constrained optimization problems. We establish its global convergence and that it converges with a linear rate when the starting point of the algorithm is feasible as well as when the starting point is infeasible. We demonstrate the effect of the scaling on the rate of convergence. We extend afterwards, the stability result of [5] to the infeasible case anf finally, we give an application to semi-infinite optimization problems. 相似文献
12.
A Globally and Superlinearly Convergent SQP Algorithm for Nonlinear Constrained Optimization 总被引:2,自引:0,他引:2
Based on a continuously differentiable exact penalty function and a regularization technique for dealing with the inconsistency of subproblems in the SQP method, we present a new SQP algorithm for nonlinear constrained optimization problems. The proposed algorithm incorporates automatic adjustment rules for the choice of the parameters and makes use of an approximate directional derivative of the merit function to avoid the need to evaluate second order derivatives of the problem functions. Under mild assumptions the algorithm is proved to be globally convergent, and in particular the superlinear convergence rate is established without assuming that the strict complementarity condition at the solution holds. Numerical results reported show that the proposed algorithm is promising. 相似文献
13.
Globally and Superlinearly Convergent QP-Free Algorithm for Nonlinear Constrained Optimization 总被引:2,自引:0,他引:2
A new, infeasible QP-free algorithm for nonlinear constrained optimization problems is proposed. The algorithm is based on a continuously differentiable exact penalty function and on active-set strategy. After a finite number of iterations, the algorithm requires only the solution of two linear systems at each iteration. We prove that the algorithm is globally convergent toward the KKT points and that, if the second-order sufficiency condition and the strict complementarity condition hold, then the rate of convergence is superlinear or even quadratic. Moreover, we incorporate two automatic adjustment rules for the choice of the penalty parameter and make use of an approximated direction as derivative of the merit function so that only first-order derivatives of the objective and constraint functions are used. 相似文献
14.
This paper presents a nonmonotone trust region algorithm for equality constrained optimization problems. Under certain conditions, we obtain not only the global convergence in the sense that every limit point is a stationary point but also the one step superlinear convergence rate. Numerical tests are also given to show the efficiency of the proposed algorithm. 相似文献
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16.
一类带非单调线搜索的信赖域算法 总被引:1,自引:0,他引:1
通过将非单调Wolfe线搜索技术与传统的信赖域算法相结合,我们提出了一类新的求解无约束最优化问题的信赖域算法.新算法在每一迭代步只需求解一次信赖域子问题,而且在每一迭代步Hesse阵的近似都满足拟牛顿条件并保持正定传递.在一定条件下,证明了算法的全局收敛性和强收敛性.数值试验表明新算法继承了非单调技术的优点,对于求解某... 相似文献
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18.
Sequential Systems of Linear Equations Algorithm for Nonlinear Optimization Problems with General Constraints 总被引:6,自引:0,他引:6
In Ref. 1, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints was proposed. At each iteration, this new algorithm only needs to solve four systems of linear equations having the same coefficient matrix, which is much less than the amount of computation required for existing SQP algorithms. Moreover, unlike the quadratic programming subproblems of the SQP algorithms (which may not have a solution), the subproblems of the SSLE algorithm are always solvable. In Ref. 2, it is shown that the new algorithm can also be used to deal with nonlinear optimization problems having both equality and inequality constraints, by solving an auxiliary problem. But the algorithm of Ref. 2 has to perform a pivoting operation to adjust the penalty parameter per iteration. In this paper, we improve the work of Ref. 2 and present a new algorithm of sequential systems of linear equations for general nonlinear optimization problems. This new algorithm preserves the advantages of the SSLE algorithms, while at the same time overcoming the aforementioned shortcomings. Some numerical results are also reported. 相似文献
19.
In this paper, we consider the least l 2-norm solution for a possibly inconsistent system of nonlinear inequalities. The objective function of the problem is only first-order continuously differentiable. By introducing a new smoothing function, the problem is approximated by a family of parameterized optimization problems with twice continuously differentiable objective functions. Then a Levenberg–Marquardt algorithm is proposed to solve the parameterized smooth optimization problems. It is proved that the algorithm either terminates finitely at a solution of the original inequality problem or generates an infinite sequence. In the latter case, the infinite sequence converges to a least l 2-norm solution of the inequality problem. The local quadratic convergence of the algorithm was produced under some conditions. 相似文献
20.
In this paper, by means of an active set strategy, we present a projected spectral gradient algorithm for solving large-scale bound constrained optimization problems. A nice property of the active set estimation technique is that it can identify the active set at the optimal point without requiring strict complementary condition, which is potentially used to solve degenerated optimization problems. Under appropriate conditions, we show that this proposed method is globally convergent. We also do some numerical experiments by using some bound constrained problems from CUTEr library. The numerical comparisons with SPG, TRON, and L-BFGS-B show that the proposed method is effective and promising. 相似文献