排序方式: 共有17条查询结果,搜索用时 15 毫秒
11.
In this paper we develop a primal-dual subgradient algorithm for preferably decomposable, generally nondifferentiable, convex programming problems, under usual regularity conditions. The algorithm employs a Lagrangian dual function along with a suitable penalty function which satisfies a specified set of properties, in order to generate a sequence of primal and dual iterates for which some subsequence converges to a pair of primal-dual optimal solutions. Several classical types of penalty functions are shown to satisfy these specified properties. A geometric convergence rate is established for the algorithm under some additional assumptions. This approach has three principal advantages. Firstly, both primal and dual solutions are available which prove to be useful in several contexts. Secondly, the choice of step sizes, which plays an important role in subgradient optimization, is guided more determinably in this method via primal and dual information. Thirdly, typical subgradient algorithms suffer from the lack of an appropriate stopping criterion, and so the quality of the solution obtained after a finite number of steps is usually unknown. In contrast, by using the primal-dual gap, the proposed algorithm possesses a natural stopping criterion. 相似文献
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Shidong Li 《Numerical Functional Analysis & Optimization》2013,34(9-10):1181-1191
We provide a characterization and construction of general frame decompositions. We show that generating all duals for a given frame amounts to finding left inverses of an one-to-one mapping. A general parametric and algebraic formula for all duals is derived. An application of the theory to Weyl-Heisenberg (WH) frames is discussed. Besides the (usual) dual frame that preserves the translation and modulation structure, we construct a class of duals that attain such a structure. We also show constructively that there are duals to WH frames which are not the translation and modulation of a single function. 相似文献
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Dončo Dimovski 《Topology and its Applications》1985,21(2):147-157
Let (W4,?W4) be a 4-manifold. Let f1,f2,…,fk:(D2,?D2)→ (W4,?W4) be transverse immersions that have spherical duals . Then there are open disjoint subsets V1, V2,…,Vk of W, such that for each 1?i?k, (a) ?Vi=V1∩?W and ?Vi is an open regular neighborhood of fi(?D2) in ?W, and (b) (Vi,?Vi,fi(?D2)) is proper homotopy equivalent to (M, ?M, d)—a standard object in which d bounds an embedded flat disk. If we could get a homeomorphism instead of a proper homotopy equivalence, then we would be able to prove a 5-dimensional s-cobordism theorem. 相似文献
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Let (x) = A(x)
, where A(x) denotes the number of square-full integers not exceeding x. In this paper, we prove that (x) = O
, which improves the exponent 4/27 obtained by Y.-C. Cai [5]. 相似文献
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Dennis Hou 《Advances in Applied Clifford Algebras》2001,11(2):265-271
For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with
the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary Clifford algebras,
followed by quaternionic vectors as a special case. All results are shown to reduce to the established method of complexifying
vector fields. For simplicity, differential forms are used rather than vector notation. 相似文献