共查询到20条相似文献,搜索用时 78 毫秒
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最近Peng等人使用新的搜索方向和自正则度量为求解线性规划问题提出了一个原始对偶内点法.本文将这个长步法延伸到凸二次规划.在线性规划情形时,原始空间和对偶空间中的尺度Newton方向是正交的,而在二次规划情形时这是不成立的.本文将处理这个问题并且证明多项式复杂性,并且得到复杂性的上界为O(n√log n log (n/ε)). 相似文献
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本文建立了目标和约束为不对称的群体多目标最优化问题的Lagrange对偶规划,在问题的联合弱有效解意义下,得到群体多目标最优化Lagrange型的弱对偶定理、基本对偶定理、直接对偶定理和逆对偶定理。 相似文献
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在一类锥约束单目标优化问题的一阶对偶模型基础之上,建立了锥约束多目标优化问题的二阶和高阶对偶模型.在广义凸性假设下,给出了弱对偶定理,在Kuhn-Tucker约束品性下,得到了强对偶定理.最后,在弱对偶定理的基础上,利用Fritz-John型必要条件建立了逆对偶定理. 相似文献
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本文提出一个二阶锥线性互补问题的长步原始对偶内点法,搜索方向由一个一般的核函数来定义.如果给出初始的严格内点,可以得到本算法的复杂性为O((1+2k)llog(lμ0/ε)). 相似文献
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数学最优化是以数学的方式来刻画和找出问题最优解的一门学科.机器学习利用数据构造预测方法,并对这些方法进行研究.介绍了机器学习中与支持向量机和稀疏重构相关的最优化模型.在此基础上,给出了三个典型最优化模型的对偶问题,并详细地讨论了对偶在求解这些问题中的应用. 相似文献
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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
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We present a new mathematical programming formulation for the Steiner minimal tree problem. We relax the integrality constraints on this formulation and transform the resulting problem (which is convex, but not everywhere differentiable) into a standard convex programming problem in conic form. We consider an efficient computation of an ε-optimal solution for this latter problem using an interior-point algorithm. 相似文献
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Qinghong Zhang 《4OR: A Quarterly Journal of Operations Research》2011,9(4):403-416
It is known that the minimal cone for the constraint system of a conic linear programming problem is a key component in obtaining
strong duality without any constraint qualification. For problems in either primal or dual form, the minimal cone can be written
down explicitly in terms of the problem data. However, due to possible lack of closure, explicit expressions for the dual
cone of the minimal cone cannot be obtained in general. In the particular case of semidefinite programming, an explicit expression
for the dual cone of the minimal cone allows for a dual program of polynomial size that satisfies strong duality. In this
paper we develop a recursive procedure to obtain the minimal cone and its dual cone. In particular, for conic problems with
so-called nice cones, we obtain explicit expressions for the cones involved in the dual recursive procedure. As an example
of this approach, the well-known duals that satisfy strong duality for semidefinite programming problems are obtained. The
relation between this approach and a facial reduction algorithm is also discussed. 相似文献
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A conic integer program is an integer programming problem with conic constraints. Many problems in finance, engineering, statistical
learning, and probabilistic optimization are modeled using conic constraints. Here we study mixed-integer sets defined by
second-order conic constraints. We introduce general-purpose cuts for conic mixed-integer programming based on polyhedral
conic substructures of second-order conic sets. These cuts can be readily incorporated in branch-and-bound algorithms that
solve either second-order conic programming or linear programming relaxations of conic integer programs at the nodes of the
branch-and-bound tree. Central to our approach is a reformulation of the second-order conic constraints with polyhedral second-order
conic constraints in a higher dimensional space. In this representation the cuts we develop are linear, even though they are
nonlinear in the original space of variables. This feature leads to a computationally efficient implementation of nonlinear
cuts for conic mixed-integer programming. The reformulation also allows the use of polyhedral methods for conic integer programming.
We report computational results on solving unstructured second-order conic mixed-integer problems as well as mean–variance
capital budgeting problems and least-squares estimation problems with binary inputs. Our computational experiments show that
conic mixed-integer rounding cuts are very effective in reducing the integrality gap of continuous relaxations of conic mixed-integer
programs and, hence, improving their solvability.
This research has been supported, in part, by Grant # DMI0700203 from the National Science Foundation. 相似文献
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This paper deals with the design of linear-phase finite impulse response (FIR) digital filters using weighted peak-constrained
least-squares (PCLS) optimization. The PCLS error design problem is formulated as a quadratically constrained quadratic semi-infinite
programming problem. An exchange algorithm with a new exchange rule is proposed to solve the problem. The algorithm provides
the approximate optimal solution after a finite number of iterations. In particular, the subproblem solved at each iteration
is a quadratically constrained quadratic programming. We can rewrite it as a conic optimization problem solvable in polynomial
time. For illustration, numerical examples are solved using the proposed algorithm. 相似文献
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Ralf Werner 《Central European Journal of Operations Research》2008,16(2):179-189
It is well known that the robust counterpart introduced by Ben-Tal and Nemirovski (Math Oper Res 23:769–805, 1998) increases
the numerical complexity of the solution compared to the original problem. Kočvara, Nemirovski and Zowe therefore introduced
in Kočvara et al. (Comput Struct 76:431–442, 2000) an approximation algorithm for the special case of robust material optimization,
called cascading. As the title already indicates, we will show that their method can be seen as an adjustment of standard exchange methods
to semi-infinite conic programming. We will see that the adjustment can be motivated by a suitable reformulation of the robust
conic problem.
相似文献
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The formulation of interior point algorithms for semidefinite programming has become an active research area, following the success of the methods for large-scale linear programming. Many interior point methods for linear programming have now been extended to the more general semidefinite case, but the initialization problem remained unsolved.In this paper we show that the initialization strategy of embedding the problem in a self-dual skew-symmetric problem can also be extended to the semidefinite case. This method also provides a solution for the initialization of quadratic programs and it is applicable to more general convex problems with conic formulation. 相似文献
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It is co-NP-complete to decide whether a given matrix is copositive or not. In this paper, this decision problem is transformed into a quadratic programming problem, which can be approximated by solving a sequence of linear conic programming problems defined on the dual cone of the cone of nonnegative quadratic functions over the union of a collection of ellipsoids. Using linear matrix inequalities (LMI) representations, each corresponding problem in the sequence can be solved via semidefinite programming. In order to speed up the convergence of the approximation sequence and to relieve the computational effort of solving linear conic programming problems, an adaptive approximation scheme is adopted to refine the union of ellipsoids. The lower and upper bounds of the transformed quadratic programming problem are used to determine the copositivity of the given matrix. 相似文献
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Yong-Jin Liu Li-Wei Zhang Yin-He Wang 《Journal of Applied Mathematics and Computing》2006,22(1-2):133-148
This paper proposes a smoothing method for symmetric conic linear programming (SCLP). We first characterize the central path conditions for SCLP problems with the help of Chen-Harker-Kanzow-Smale smoothing function. A smoothing-type algorithm is constructed based on this characterization and the global convergence and locally quadratic convergence for the proposed algorithm are demonstrated. 相似文献
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In the conic optimization problems, it is well-known that a positive duality gap may occur, and that solving such a problem is numerically difficult or unstable. For such a case, we propose a facial reduction algorithm to find a primal–dual pair of conic optimization problems having the zero duality gap and the optimal value equal to one of the original primal or dual problems. The conic expansion approach is also known as a method to find such a primal–dual pair, and in this paper we clarify the relationship between our facial reduction algorithm and the conic expansion approach. Our analysis shows that, although they can be regarded as dual to each other, our facial reduction algorithm has ability to produce a finer sequence of faces of the cone including the feasible region. A simple proof of the convergence of our facial reduction algorithm for the conic optimization is presented. We also observe that our facial reduction algorithm has a practical impact by showing numerical experiments for graph partition problems; our facial reduction algorithm in fact enhances the numerical stability in those problems. 相似文献