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51.
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
52.
Wiesł Nizioł 《Compositio Mathematica》2001,129(2):123-147
We define and study a candidate for 'arithmetic' cohomology theory with values in crystalline p-adic smooth sheaves. We show that it injects into arithmetic étale cohomology and prove a duality result. 相似文献
53.
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
54.
Conservative linear equations arise in many areas of application, including continuum mechanics or high-frequency geometrical optics approximations. This kind of equation admits most of the time solutions which are only bounded measures in the space variable known as duality solutions. In this paper, we study the convergence of a class of finite-difference numerical schemes and introduce an appropriate concept of consistency with the continuous problem. Some basic examples including computational results are also supplied.
55.
本利用次微分建立了多目标规划的一个新的对偶问题,并给出其弱、强和逆对偶性,得到了一个新的次梯度的定义,并用其建立了一个新的对偶问题。 相似文献
56.
Y. C. Cheng 《Journal of Optimization Theory and Applications》1987,53(2):237-246
A new dual gradient method is given to solve linearly constrained, strongly convex, separable mathematical programming problems. The dual problem can be decomposed into one-dimensional problems whose solutions can be computed extremely easily. The dual objective function is shown to have a Lipschitz continuous gradient, and therefore a gradient-type algorithm can be used for solving the dual problem. The primal optimal solution can be obtained from the dual optimal solution in a straightforward way. Convergence proofs and computational results are given. 相似文献
57.
Necessary and sufficient conditions in constrained optimization 总被引:22,自引:0,他引:22
Additional conditions are attached to the Kuhn-Tucker conditions giving a set of conditions which are both necessary and sufficient
for optimality in constrained optimization, under appropriate constraint qualifications. Necessary and sufficient conditions
are also given for optimality of the dual problem. Duality and converse duality are treated accordingly. 相似文献
58.
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
59.
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
60.
Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic in Lorentzian conformal geometry which parallels the theory of Willmore surfaces in S4, are studied in this paper. We define two kinds of transforms for such a surface, which produce the so-called left/right polar surfaces and the adjoint surfaces. These new surfaces are again conformal Willmore surfaces. For them the interesting duality theorem holds. As an application spacelike Willmore 2-spheres are classified. Finally we construct a family of homogeneous spacelike Willmore tori. 相似文献