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151.
We study the dual problems associated with the robust counterparts of uncertain convex programs. We show that while the primal robust problem corresponds to a decision maker operating under the worst possible data, the dual problem corresponds to a decision maker operating under the best possible data. 相似文献
152.
The stationary and nonstationary rotating Navier-Stokes equations with mixed boundary conditions are investigated in this paper. The existence and uniqueness of the solutions are obtained by the Galerkin approximation method. Next, θ-scheme of operator splitting algorithm is applied to rotating Navier-Stokes equations and two subproblems are derived. Finally, the computational algorithms for these subproblems are provided. 相似文献
153.
We consider an approach for ex post evaluation of approximate solutions obtained by a well known simple greedy method for
set packing. A performance bound is derived that is a function of the highest average reward per item over subsets as well
as the number of allocated subsets and ground items. This a posterior bound can enable much revelation of optimality when
the solution is near optimal. One of the advantages of the ex post analysis is that it does not require computing the optimal
solution to the LP relaxation. The ex post bound will not be guaranteed to reveal substantial levels of optimality for all
problem instances but can be a useful tool that is complementary to other traditional methods for ex post evaluation for the
set packing problem. 相似文献
154.
Log-Sigmoid Multipliers Method in Constrained Optimization 总被引:10,自引:0,他引:10
Roman A. Polyak 《Annals of Operations Research》2001,101(1-4):427-460
In this paper we introduced and analyzed the Log-Sigmoid (LS) multipliers method for constrained optimization. The LS method is to the recently developed smoothing technique as augmented Lagrangian to the penalty method or modified barrier to classical barrier methods. At the same time the LS method has some specific properties, which make it substantially different from other nonquadratic augmented Lagrangian techniques.We established convergence of the LS type penalty method under very mild assumptions on the input data and estimated the rate of convergence of the LS multipliers method under the standard second order optimality condition for both exact and nonexact minimization.Some important properties of the dual function and the dual problem, which are based on the LS Lagrangian, were discovered and the primal–dual LS method was introduced. 相似文献
155.
A.H. Bentbib 《Numerical Algorithms》1999,21(1-4):79-86
We propose the interval version of the conjugate directions method, to solve the problem of linear systems, with symmetric
and positive definite interval matrix A, and a right-hand side interval vector b.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
156.
Marc Chardin Kamran Divaani-Aazar 《Proceedings of the American Mathematical Society》2008,136(8):2749-2754
We prove a duality theorem for graded algebras over a field that implies several known duality results: graded local duality, versions of Serre duality for local cohomology and of Suzuki duality for generalized local cohomology, and Herzog-Rahimi bigraded duality.
157.
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
158.
160.
Qinghong Zhang 《Central European Journal of Operations Research》2008,16(2):205-213
Recently, a semidefinite and semi-infinite linear programming problem (SDSIP), its dual (DSDSIP), and uniform LP duality between
(SDSIP) and (DSDSIP) were proposed and studied by Li et al. (Optimization 52:507–528, 2003). In this paper, we show that (SDSIP)
is an ordinary linear semi-infinite program and, therefore, all the existing results regarding duality and uniform LP duality
for linear semi-infinite programs can be applied to (SDSIP). By this approach, the main results of Li et al. (Optimization
52:507–528, 2003) can be obtained easily. 相似文献