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101.
We use the improved Faddeev-Jackiw quantization method to quantize the electromagnetic field and its Lagrange multiplier fields. The method's comparison with the usual Faddeev-Jackiw method and the Dirac method is given. We show that this method is equivalent to the Dirac method and also retains all the merits of the usual Faddeev-Jackiw method. Moreover, it is simpler than the usual one if one needs to obtain new secondary constraints. Therefore, the improved Faddeev-Jackiw method is essential. Meanwhile, we find the new meaning of the Lagrange multipliers and explain the Faddeev-Jackiw generalized brackets concerning the Lagrange multipliers. 相似文献
102.
M. Durea 《Journal of Mathematical Analysis and Applications》2008,348(2):589-606
The aim of this paper is to point out some sufficient constraint qualification conditions ensuring the boundedness of a set of Lagrange multipliers for vectorial optimization problems in infinite dimension. In some (smooth) cases these conditions turn out to be necessary for the existence of multipliers as well. 相似文献
103.
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
104.
Nguyen Thi Van Hang 《Numerical Functional Analysis & Optimization》2013,34(3):364-386
This article shows that finite-dimensional multiplier rules, which are based on the limiting subdifferential, can be proved by Ekeland's variational principle and some basic calculus tools of the generalized differentiation theory introduced by B. S. Mordukhovich. Consequences of a limiting constraint qualification, which yields the normal form of the multiplier rules, stability and calmness of optimization problems, are investigated in detail. 相似文献
105.
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
106.
Ajit Patel Amiya K. Pani Neela Nataraj 《Numerical Methods for Partial Differential Equations》2008,24(6):1460-1484
In this article a standard mortar finite element method and a mortar element method with Lagrange multiplier are used for spatial discretization of a class of parabolic initial‐boundary value problems. Optimal error estimates in L∞(L2) and L∞(H1)‐norms for semidiscrete methods for both the cases are established. The key feature that we have adopted here is to introduce a modified elliptic projection. In the standard mortar element method, a completely discrete scheme using backward Euler scheme is discussed and optimal error estimates are derived. The results of numerical experiments support the theoretical results obtained in this article. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 相似文献
107.
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
108.
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
109.
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
110.
P. P. J. Van Den Bosch F. A. Lootsma 《Journal of Optimization Theory and Applications》1987,55(2):313-326
We investigate methods for solving high-dimensional nonlinear optimization problems which typically occur in the daily scheduling of electricity production: problems with a nonlinear, separable cost function, lower and upper bounds on the variables, and an equality constraint to satisfy the demand. If the cost function is quadratic, we use a modified Lagrange multiplier technique. For a nonquadratic cost function (a penalty function combining the original cost function and certain fuel constraints, so that it is generally not separable), we compare the performance of the gradient-projection method and the reduced-gradient method, both with conjugate search directions within facets of the feasible set. Numerical examples at the end of the paper demonstrate the effectiveness of the gradient-projection method to solve problems with hundreds of variables by exploitation of the special structure. 相似文献