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61.
A. V. Zykina 《Computational Mathematics and Mathematical Physics》2008,48(11):1971-1980
The concept of inverse complementarity for a parametric family of optimization problems is introduced. This concept is an
effective tool for solving complicated applied problems arising in socioeconomic systems. As an example, a nonlinear resource
deficit model is constructed in which the equilibrium is characterized by an external market value of resources coinciding
with internal objectively determined resource estimates. An extraproximal method is proposed for computing an equilibrium
solution. The convergence of the method is proved.
Original Russian Text. A.V. Zykina, 2008, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2008,
Vol. 48, No. 11, pp. 1968–1978. 相似文献
62.
修正了文[1]中的错误,在其基础上讨论了凸规划的Lagrange对偶,Subgradient对偶及Wolfe对偶等四种对偶模型之间的关系,给出了它们之间等价的条件. 相似文献
63.
O. Briant C. Lemaréchal Ph. Meurdesoif S. Michel N. Perrot F. Vanderbeck 《Mathematical Programming》2008,113(2):299-344
When a column generation approach is applied to decomposable mixed integer programming problems, it is standard to formulate
and solve the master problem as a linear program. Seen in the dual space, this results in the algorithm known in the nonlinear
programming community as the cutting-plane algorithm of Kelley and Cheney-Goldstein. However, more stable methods with better
theoretical convergence rates are known and have been used as alternatives to this standard. One of them is the bundle method;
our aim is to illustrate its differences with Kelley’s method. In the process we review alternative stabilization techniques
used in column generation, comparing them from both primal and dual points of view. Numerical comparisons are presented for
five applications: cutting stock (which includes bin packing), vertex coloring, capacitated vehicle routing, multi-item lot
sizing, and traveling salesman. We also give a sketchy comparison with the volume algorithm.
This research has been supported by Inria New Investigation Grant “Convex Optimization and Dantzig-Wolfe Decomposition”. 相似文献
64.
Radu Ioan Bo? Sorin-Mihai Grad 《Journal of Mathematical Analysis and Applications》2008,337(2):1315-1325
We give some necessary and sufficient conditions which completely characterize the strong and total Lagrange duality, respectively, for convex optimization problems in separated locally convex spaces. We also prove similar statements for the problems obtained by perturbing the objective functions of the primal problems by arbitrary linear functionals. In the particular case when we deal with convex optimization problems having infinitely many convex inequalities as constraints the conditions we work with turn into the so-called Farkas-Minkowski and locally Farkas-Minkowski conditions for systems of convex inequalities, recently used in the literature. Moreover, we show that our new results extend some existing ones in the literature. 相似文献
65.
We show that the Priestley sum of finite trees contains no cyclic finite poset.
The first author would like to express his thanks for support from project LN 1M0021620808 of the Ministry of Education of
the Czech Republic. The second author would like to express his thanks for support from project 1M0021620808 of the Ministry
of Education of the Czech Republic, from the NSERC of Canada and from a PROF grant from the University of Denver. The third
author would like to express his thanks for the support from the NSERC of Canada and for partial support from the project
1M0021620808 of the Ministry of Education of the Czech Republic. 相似文献
66.
用一种统一的方式,讨论了线性规划问题中常用的罚函数方法及其对偶性.并将这种方法应用到等式约束二次规划问题中. 相似文献
67.
68.
Wolfe Duality for Interval-Valued Optimization 总被引:1,自引:0,他引:1
H. C. Wu 《Journal of Optimization Theory and Applications》2008,138(3):497-509
Weak and strong duality theorems in interval-valued optimization problem based on the formulation of the Wolfe primal and
dual problems are derived. The solution concepts of the primal and dual problems are based on the concept of nondominated
solution employed in vector optimization problems. The concepts of no duality gap in the weak and strong sense are also introduced,
and strong duality theorems in the weak and strong sense are then derived. 相似文献
69.
Let E be a real reflexive Banach space having a weakly continuous duality mapping Jφ with a gauge function φ, and let K be a nonempty closed convex subset of E. Suppose that T is a non‐expansive mapping from K into itself such that F (T) ≠ ??. For an arbitrary initial value x0 ∈ K and fixed anchor u ∈ K, define iteratively a sequence {xn } as follows: xn +1 = αn u + βn xn + γn Txn , n ≥ 0, where {αn }, {βn }, {γn } ? (0, 1) satisfies αn +βn + γn = 1, (C 1) limn →∞ αn = 0, (C 2) ∑∞n =1 αn = ∞ and (B) 0 < lim infn →∞ βn ≤ lim supn →∞ βn < 1. We prove that {xn } converges strongly to Pu as n → ∞, where P is the unique sunny non‐expansive retraction of K onto F (T). We also prove that the same conclusions still hold in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm or in a uniformly smooth Banach space. Our results extend and improve the corresponding ones by C. E. Chidume and C. O. Chidume [Iterative approximation of fixed points of non‐expansive mappings, J. Math. Anal. Appl. 318 , 288–295 (2006)], and develop and complement Theorem 1 of T. H. Kim and H. K. Xu [Strong convergence of modified Mann iterations, Nonlinear Anal. 61 , 51–60 (2005)]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
70.