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Proximal extrapolated gradient methods for variational inequalities. 变分不等式的近端外推梯度方法。
IF 2.2 3区 数学 Q1 Mathematics
Optimization Methods & Software
Pub Date : 2017-03-21 eCollection Date: 2018-01-01 DOI: 10.1080/10556788.2017.1300899
Yu Malitsky

The paper concerns with novel first-order methods for monotone variational inequalities. They use a very simple linesearch procedure that takes into account a local information of the operator. Also, the methods do not require Lipschitz continuity of the operator and the linesearch procedure uses only values of the operator. Moreover, when the operator is affine our linesearch becomes very simple, namely, it needs only simple vector-vector operations. For all our methods, we establish the ergodic convergence rate. In addition, we modify one of the proposed methods for the case of a composite minimization. Preliminary results from numerical experiments are quite promising.

本文研究单调变分不等式的一阶新方法。他们使用一种非常简单的线路搜索程序，考虑到操作员的本地信息。此外，该方法不需要算子的Lipschitz连续性，并且直线研究过程仅使用算子的值。此外，当算子是仿射时，我们的直线研究变得非常简单，即只需要简单的向量-向量运算。对于所有的方法，我们都建立了遍历收敛率。此外，我们还对其中一种方法进行了修改，以适应复合最小化的情况。数值实验的初步结果很有希望。
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引用次数: 53
Enhanced Bounding Techniques to Reduce the Protein Conformational Search Space. 减少蛋白质构象搜索空间的增强边界技术。
IF 2.2 3区 数学 Q1 Mathematics
Optimization Methods & Software
Pub Date : 2009-08-01 DOI: 10.1080/10556780902753486
Scott R McAllister, Christodoulos A Floudas

The complexity and enormous size of the conformational space that must be explored for the protein tertiary structure prediction problem has led to the development of a wide assortment of algorithmic approaches. In this study, we apply state-of-the-art tertiary structure prediction algorithms and instead focus on the development of bounding techniques to reduce the conformational search space. Dihedral angle bounds on the ϕ and ψ angles are established based on the predicted secondary structure and studies of the allowed regions of ϕ/ψ space. Distance bounds are developed based on predicted secondary structure information (including β-sheet topology predictions) to further reduce the search space. This bounding strategy is entirely independent of the degree of homology between the target protein and the database of proteins with experimentally-determined structures. The proposed approach is applied to the structure prediction of protein G as an illustrative example, yielding a significantly higher number of near-native protein tertiary structure predictions.

蛋白质三级结构预测问题必须探索的构象空间的复杂性和巨大规模导致了各种算法方法的发展。在这项研究中，我们应用了最先进的三级结构预测算法，转而专注于边界技术的开发，以减少构象搜索空间。基于预测的二次结构和对Γ/ψ空间允许区域的研究，建立了Γ和ψ角上的二面角边界。基于预测的二次结构信息（包括β-薄板拓扑预测）开发距离边界，以进一步减少搜索空间。这种结合策略完全独立于靶蛋白和具有实验确定结构的蛋白质数据库之间的同源性程度。所提出的方法被应用于蛋白质G的结构预测，作为一个说明性的例子，产生了显著更高数量的近天然蛋白质三级结构预测。
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引用次数: 5
A dual parameterization approach to linear-quadratic semi-infinite programming problems 线性二次半无限规划问题的对偶参数化方法
IF 2.2 3区 数学 Q1 Mathematics
Optimization Methods & Software
Pub Date : 1999-01-01 DOI: 10.1080/10556789908805725
Y. Liu, K. Teo, S. Ito
Semi-infinite programming problems are special optimization problems in which a cost is to be minimized subject to infinitely many constraints. This class of problems has many real-world applications. In this paper, we consider a class of linear-quadratic semi-infinite programming problems. Using the duality theory, the dual problem is obtained, where the decision variables are measures. A new parameterization scheme is developed for approximating these measures. On this bases, an efficient algorithm for computing the solution of the dual problem is obtained. Rigorous convergence results are given to support the algorithm. The solution of the primal problem is easily obtained from that of the dual problem. For illustration, three numerical examples are included.
半无限规划问题是一种特殊的优化问题，其目标是在无限多个约束条件下使成本最小化。这类问题有许多实际应用。本文研究了一类线性二次半无限规划问题。利用对偶理论，得到了决策变量为测度的对偶问题。提出了一种新的参数化方案来逼近这些度量。在此基础上，给出了一种计算对偶问题解的有效算法。给出了严格的收敛结果来支持该算法。原始问题的解很容易由对偶问题的解得到。为了说明，本文给出了三个数值例子。
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引用次数: 13
A combined relaxation method for decomposable variational inequalities 可分解变分不等式的组合松弛法
IF 2.2 3区 数学 Q1 Mathematics
Optimization Methods & Software
Pub Date : 1999-01-01 DOI: 10.1080/10556789908805735
I. Konnov
An iterative method based on combining, modifying and generalizing different relaxation subgradient methods is proposed for solving variational inequality problems. For certain structured problems this method leads to a decomposition scheme. Convergence of the method is proved under weak assumptions. In particular, the main mapping need not be single-valued or monotone.
针对变分不等式问题，提出了一种基于组合、修正和推广不同松弛子梯度方法的迭代求解方法。对于某些结构化问题，这种方法导致分解方案。在弱假设条件下证明了该方法的收敛性。特别是，主映射不需要是单值的或单调的。
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引用次数: 9
Computing Wardropian equilibria in a complementarity framework 互补框架下的衣柜均衡计算
IF 2.2 3区 数学 Q1 Mathematics
Optimization Methods & Software
Pub Date : 1999-01-01 DOI: 10.1080/10556789908805733
M. Ferris, A. Meeraus, T. Rutherford
This note considers alternative methods for computing Wadropian (traffic network) equilibria using a multicommodity formulation in nonlinear program and complementarity formats. These methods compute exact equilibria, they are efficient and they can be implemented with standard modeling software.
本文考虑使用非线性规划和互补格式的多商品公式计算交通网络平衡的替代方法。这些方法计算精确均衡，效率高，可以用标准的建模软件实现。
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引用次数: 45
A note on the Nesterov-Todd and the Kojima-Shindoh-hara search directions in semidefinite programming 半定规划中Nesterov-Todd和Kojima-Shindoh-hara搜索方向的注释
IF 2.2 3区 数学 Q1 Mathematics
Optimization Methods & Software
Pub Date : 1999-01-01 DOI: 10.1080/10556789908805746
M. Kojima, M. Shida, Susumu Shindoh
This short note shows that the Nesterov-Todd search direction used in primal-dual interior-point methods for semidefinite programs belongs to the family of search directions proposed by Kojima, Shindoh and Hara.
这篇简短的笔记表明，用于半定规划的原始对偶内点法的Nesterov-Todd搜索方向属于Kojima、Shindoh和Hara提出的搜索方向族。
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引用次数: 17
Regularized Symmetric Indefinite Systems in Interior Point Methods for Linear and Quadratic Optimization 正则对称不定系统的线性和二次优化的内点法
IF 2.2 3区 数学 Q1 Mathematics
Optimization Methods & Software
Pub Date : 1999-01-01 DOI: 10.1080/10556789908805754
A. Altman, J. Gondzio
This paper presents linear algebra techniques used in the implementation of an interior point method for solving linear programs and convex quadratic programs with linear constraint. The new regularization techniques for Newton equation system applicable to both symmetric positive definite and symmetric indefinite systems are described. They transform the latter to quasidefinite systems known to be strongly factorizable to a form of Cholesky-like factorization.
本文介绍了求解线性规划和带线性约束的凸二次规划的内点法的线性代数技术。描述了牛顿方程组的正则化新技术，该技术适用于对称正定系统和对称不定系统。它们将后者转化为准定系统，这些准定系统是强可因式分解的一种形式。
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引用次数: 178
A study of search directions in primal-dual interior-point methods for semidefinite programming 半定规划中原始-对偶内点法搜索方向的研究
IF 2.2 3区 数学 Q1 Mathematics
Optimization Methods & Software
Pub Date : 1999-01-01 DOI: 10.1080/10556789908805745
M. Todd
We discuss several different search directions which can be used in primal-dual interior-point methods for semidefinite programming problems and investigate their theoretical properties, including scale invariance, primal-dual symmetry, and whether they always generate well-defined directions. Among the directions satisfying all but at most two of these desirable properties are the Alizadeh-Haeberly-Overton, Helmberg-Rendl-Vanderbei-Wolkowicz/Kojima-Shindoh-HaralMonteiro, Nesterov-Todd, Gu, and Toh directions, as well as directions we will call the MTW and Half directions. The first five of these appear to be the best in our limited computational testing also.
讨论了用于半确定规划问题的原始-对偶内点方法的几种不同的搜索方向，并研究了它们的理论性质，包括尺度不变性、原始-对偶对称性以及它们是否总是生成良好定义的方向。在满足所有这些理想性质的方向中，除了最多两个之外，还有alizadeh - haebery - overton, Helmberg-Rendl-Vanderbei-Wolkowicz/Kojima-Shindoh-HaralMonteiro, Nesterov-Todd, Gu和Toh方向，以及我们称之为MTW和Half方向。在我们有限的计算测试中，前五个似乎也是最好的。
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引用次数: 122
A hybrid Josephy — Newton method for solving box constrained variational equality roblems via the D-gap function 利用D-gap函数求解盒约束变分等式问题的约瑟夫-牛顿混合方法
IF 2.2 3区 数学 Q1 Mathematics
Optimization Methods & Software
Pub Date : 1999-01-01 DOI: 10.1080/10556789908805734
Jiming Peng, Christian Kanzowb, M. Fukushima
A box constrained variational inequality problem can be reformulated as an unconstrained minimization problem through the D-gap function. Some basic properties of the affine variational inequality subproblems in the classical Josephy-Newton method are studied. A hybrid Josephy-Newton method is then proposed for minimizing the D-gap function. Under suitable conditions, the algorithm is shown to be globally convergent and locally quadratically convergent. Some numerical results are also presented.
盒约束变分不等式问题可以通过D-gap函数重新表述为无约束最小化问题。研究了经典约瑟夫-牛顿方法中仿射变分不等式子问题的一些基本性质。然后提出了一种混合约瑟夫-牛顿法来最小化D-gap函数。在适当的条件下，该算法具有全局收敛性和局部二次收敛性。给出了一些数值结果。
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引用次数: 17
On self-concordant convex–concave functions 关于自调和凸凹函数
IF 2.2 3区 数学 Q1 Mathematics
Optimization Methods & Software
Pub Date : 1999-01-01 DOI: 10.1080/10556789908805755
A. Nemirovski
In this paper, we introduce the notion of a self-concordant convex-concave function, establish basic properties of these functions and develop a path-following interior point method for approximating saddle points of “sufficiently well-behaved” convex-concave functions—those which admit natural self-concordant convex-concave regularizations. The approach is illustrated by its applications to developing an exterior penalty polynomial time method for Semidefinite Programming and to the problem of inscribing the largest volume ellipsoid into a given polytope.
本文引入了自调和凸凹函数的概念，建立了这些函数的基本性质，并发展了一种逼近“足够好”凸凹函数鞍点的路径跟踪内点法，这些凸凹函数承认自然的自调和凸凹正则化。该方法在半定规划的外罚多项式时间法和在给定多面体上刻入最大体积椭球体问题中的应用说明了该方法的可行性。
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引用次数: 17
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