共查询到20条相似文献,搜索用时 0 毫秒
1.
Chek Beng Chua 《Foundations of Computational Mathematics》2007,7(3):271-302
Given any open convex cone K, a logarithmically homogeneous, self-concordant barrier for K, and any positive real number r
< 1, we associate, with each direction
, a second-order cone
containing K. We show that K is the interior of the intersection of the second-order cones
, as x ranges over all directions in K. Using these second-order cones as approximations to cones of symmetric, positive definite
matrices, we develop a new polynomial-time primal-dual interior-point algorithm for semidefinite programming. The algorithm
is extended to symmetric cone programming via the relation between symmetric cones and Euclidean Jordan algebras. 相似文献
2.
给出一对锥约束多目标非线性规划的二阶对称对偶问题,以及二阶F凸函数类的概念.在二阶F凸假设下证明了真有效解的对偶性质———弱对偶性、强对偶性及逆对偶性. 相似文献
3.
4.
5.
Acta Mathematicae Applicatae Sinica, English Series - In this paper, we present a neighborhood following primal-dual interior-point algorithm for solving symmetric cone convex quadratic programming... 相似文献
6.
We discuss two families of valid inequalities for linear mixed integer programming problems with cone constraints of arbitrary order, which arise in the context of stochastic optimization with downside risk measures. In particular, we extend the results of Atamtürk and Narayanan (Math. Program., 122:1–20, 2010, Math. Program., 126:351–363, 2011), who developed mixed integer rounding cuts and lifted cuts for mixed integer programming problems with second-order cone constraints. Numerical experiments conducted on randomly generated problems and portfolio optimization problems with historical data demonstrate the effectiveness of the proposed methods. 相似文献
7.
J. X. da Cruz Neto O. P. Ferreira P. R. Oliveira R. C. M. Silva 《Journal of Optimization Theory and Applications》2008,139(2):227-242
The relationships among the central path in the context of semidefinite programming, generalized proximal-point method and
Cauchy trajectory in a Riemannian manifolds is studied in this paper. First, it is proved that the central path associated
to a general function is well defined. The convergence and characterization of its limit point is established for functions
satisfying a certain continuity property. Also, the generalized proximal-point method is considered and it is proved that
the correspondingly generated sequence is contained in the central path. As a consequence, both converge to the same point.
Finally, it is proved that the central path coincides with the Cauchy trajectory in a Riemannian manifold.
This work was supported in part by CNPq Grant 302618/2005-8, by PRONEX(CNPq), CAPES-PICDT and FUNAPE/UFG. 相似文献
8.
9.
The Q method of semidefinite programming, developed by Alizadeh, Haeberly and Overton, is extended to optimization problems over
symmetric cones. At each iteration of the Q method, eigenvalues and Jordan frames of decision variables are updated using Newton’s method. We give an interior point
and a pure Newton’s method based on the Q method. In another paper, the authors have shown that the Q method for second-order cone programming is accurate. The Q method has also been used to develop a “warm-starting” approach for second-order cone programming. The machinery of Euclidean
Jordan algebra, certain subgroups of the automorphism group of symmetric cones, and the exponential map is used in the development
of the Newton method. Finally we prove that in the presence of certain non-degeneracies the Jacobian of the Newton system
is nonsingular at the optimum. Hence the Q method for symmetric cone programming is accurate and can be used to “warm-start” a slightly perturbed symmetric cone program. 相似文献
10.
Jean-Pierre Dedieu Gregorio Malajovich Mike Shub 《Foundations of Computational Mathematics》2005,5(2):145-171
We prove a linear bound on the average total curvature of the
central path of linear programming theory in terms of the number
of independent variables of the primal problem, and independent of
the number of constraints. 相似文献
11.
V. G. Zhadan 《Computational Mathematics and Mathematical Physics》2018,58(2):207-214
A linear cone programming problem containing among the constraints a second-order cone is considered. For solving this problem, a primal Newton method which is constructed with the help of the optimality conditions is proposed. Local convergence of this method is proven. 相似文献
12.
13.
14.
On a Commutative Class of Search Directions for Linear Programming over Symmetric Cones 总被引:3,自引:0,他引:3
The commutative class of search directions for semidefinite programming was first proposed by Monteiro and Zhang (Ref. 1). In this paper, we investigate the corresponding class of search directions for linear programming over symmetric cones, which is a class of convex optimization problems including linear programming, second-order cone programming, and semidefinite programming as special cases. Complexity results are established for short-step, semilong-step, and long-step algorithms. Then, we propose a subclass of the commutative class for which we can prove polynomial complexities of the interior-point method using semilong steps and long steps. This subclass still contains the Nesterov–Todd direction and the Helmberg–Rendl–Vanderbei–Wolkowicz/Kojima–Shindoh–Hara/Monteiro direction. An explicit formula to calculate any member of the class is also given. 相似文献
15.
多目标规划锥有效解的最优性条件 总被引:1,自引:0,他引:1
该文提出了广义锥凸向量函数以及向量函数关于锥八的下降、不变、非升、非降方向集等概念.在讨论它们的性质和判别条件的基础上,给出了决策可行集中的点为锥八一有效解的一系列充分必要条件. 相似文献
16.
F. Maggioni F. A. Potra M. I. Bertocchi E. Allevi 《Journal of Optimization Theory and Applications》2009,143(2):309-328
We propose a two-stage stochastic second-order cone programming formulation of the semidefinite stochastic location-aided
routing (SLAR) model, described in Ariyawansa and Zhu (Q. J. Oper. Res. 4(3), 239–253, 2006). The aim is to provide a sender node S with an algorithm for optimally determining a region that is expected to contain
a destination node D (the expected zone). The movements of the destination node are represented by ellipsoid scenarios, randomly generated by
uniform and normal distributions in a neighborhood of the starting position of the destination node. By using a second-order
cone model, we are able to solve problems with a much larger number of scenarios (20250) than it is possible with the semidefinite
model (500). The use of a larger number of scenarios allows for the computation of a new expected zone, that may be very effective
in practical applications, and for obtaining stability results for the optimal first-stage solutions and the optimal cost
function values. 相似文献
17.
本文讨论了二阶凸和二阶凹条件下的二阶对称对偶问题,并利用有效性和真有效性概念证明了弱对偶、强对偶、逆对偶及自对偶定理。 相似文献
18.
19.
Baha Alzalg 《Journal of Optimization Theory and Applications》2014,163(1):148-164
Jin et al. (in J. Optim. Theory Appl. 155:1073–1083, 2012) proposed homogeneous self-dual algorithms for stochastic semidefinite programs with finite event space. In this paper, we utilize their work to derive homogeneous self-dual algorithms for stochastic second-order cone programs with finite event space. We also show how the structure in the stochastic second-order cone programming problems may be exploited so that the algorithms developed for these problems have less complexity than the algorithms developed for stochastic semidefinite programs mentioned above. 相似文献
20.
基于不可行内点法和预估-校正算法的思想,提出两个新的求解二阶锥规划的内点预估-校正算法.其预估方向分别是Newton方向和Euler方向,校正方向属于Alizadeh-Haeberly-Overton(AHO)方向的范畴.算法对于迭代点可行或不可行的情形都适用.主要构造了一个更简单的中心路径的邻域,这是有别于其它内点预估-校正算法的关键.在一些假设条件下,算法具有全局收敛性、线性和二次收敛速度,并获得了O(rln(ε0/ε))的迭代复杂性界,其中r表示二阶锥规划问题所包含的二阶锥约束的个数.数值实验结果表明提出的两个算法是有效的. 相似文献