共查询到9条相似文献,搜索用时 15 毫秒
1.
Xinsheng Xu Chuangyin Dang Felix T. S. Chan Yongli Wang 《Numerical Functional Analysis & Optimization》2019,40(1):1-18
This article introduces a smoothing technique to the l1 exact penalty function. An application of the technique yields a twice continuously differentiable penalty function and a smoothed penalty problem. Under some mild conditions, the optimal solution to the smoothed penalty problem becomes an approximate optimal solution to the original constrained optimization problem. Based on the smoothed penalty problem, we propose an algorithm to solve the constrained optimization problem. Every limit point of the sequence generated by the algorithm is an optimal solution. Several numerical examples are presented to illustrate the performance of the proposed algorithm. 相似文献
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Zhiqing Meng Chuangyin Dang Xiaoqi Yang 《Computational Optimization and Applications》2006,35(3):375-398
In this paper we propose two methods for smoothing a nonsmooth square-root exact penalty function for inequality constrained
optimization. Error estimations are obtained among the optimal objective function values of the smoothed penalty problem,
of the nonsmooth penalty problem and of the original optimization problem. We develop an algorithm for solving the optimization
problem based on the smoothed penalty function and prove the convergence of the algorithm. The efficiency of the smoothed
penalty function is illustrated with some numerical examples, which show that the algorithm seems efficient. 相似文献
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We show that for a sequence in a Banach space, the property of being stable under large perturbations characterizes the property of being equivalent to the unit vector basis of l
1. We show that a normalized unconditional basic sequence in l
1 that is semi-normalized in l
is equivalent to the standard unit vector basis of l
1. 相似文献
5.
Tadeusz Antczak 《Applied mathematics and computation》2011,217(15):6652-6662
A new exact penalty function method, called the l1 exact exponential penalty function method, is introduced. In this approach, the so-called the exponential penalized optimization problem with the l1 exact exponential penalty function is associated with the original optimization problem with both inequality and equality constraints. The l1 exact exponential penalty function method is used to solve nonconvex mathematical programming problems with r-invex functions (with respect to the same function η). The equivalence between sets of optimal solutions of the original mathematical programming problem and of its associated exponential penalized optimization problem is established under suitable r-invexity assumption. Also lower bounds on the penalty parameter are given, for which above these values, this result is true. 相似文献
6.
Jennifer Taback 《Geometriae Dedicata》2003,102(1):179-195
We show that PSL2(Z[1/p]) admits a combing with bounded asynchronous width, and use this combing to show that PSL2(Z[1/p]) has an exponential Dehn function. As a corollary, PSL2(Z[1/p]) has solvable word problem and is not an automatic group. 相似文献
7.
Tadeusz Antczak 《Journal of Mathematical Analysis and Applications》2006,322(2):971-989
A new method is used for solving nonlinear multiobjective fractional programming problems having V-invex objective and constraint functions with respect to the same function η. In this approach, an equivalent vector programming problem is constructed by a modification of the objective fractional function in the original nonlinear multiobjective fractional problem. Furthermore, a modified Lagrange function is introduced for a constructed vector optimization problem. By the help of the modified Lagrange function, saddle point results are presented for the original nonlinear fractional programming problem with several ratios. Finally, a Mond-Weir type dual is associated, and weak, strong and converse duality results are established by using the introduced method with a modified function. To obtain these duality results between the original multiobjective fractional programming problem and its original Mond-Weir duals, a modified Mond-Weir vector dual problem with a modified objective function is constructed. 相似文献
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Numerical methods of finding the roots of a system of non-linear algebraic equations are treated in this paper. This paper attempts to give an answer to the selection of the most efficient method in a complex problem of Celestial Dynamics, the so-called ring problem of (N + 1) bodies. We apply Newton and Broyden’s method to these problems and we investigate, by means of their use, the planar equilibrium points, the five equilibrium zones, which are symbolized by A1, A2, B, C2, and C1 (by order of appearance from the center O to the periphery of the imaginary circle on which the primaries lie) [T.J. Kalvouridis, A planar case of the N + 1 body problem: the ring problem. Astrophys. Space Sci. 260 (3) (1999) 309-325], and the attracting regions of the system. The efficiency of these methods is studied through a comparative process. The obtained results are demonstrated in figures and are discussed. 相似文献