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1.
The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues, to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a hot start. Starting at such a hot start, at mostO(In In
-1) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, >0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that onlyO(In
-1)O(In In
-1) Newton steps are required to reach an -approximation to the solution from any hot start. In order to reach the hot start, one has to perform
Newton steps, wherem characterizes the size of the problem andC>0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.Partially supported by NASA Grant NAG3-1397 and National Science Foundation Grant DMS-9403218. 相似文献
2.
In this paper we show that the weakly -Engel conditions are closely related to the existance of normal -complements; while the -Engel conditions are closely related to the -nilpotent groups.AMS Subject Classification (2000): 20D20 相似文献
3.
J. C. Liu 《Journal of Optimization Theory and Applications》1991,69(1):153-167
Necessary Kuhn-Tucker conditions up to precision without constraint qualification for -Pareto optimality of multiobjective programming are derived. This article suggests the establishment of a Wolfe-type -duality theorem for nondifferentiable, nonconvex, multiobjective minimization problems. The -vector Lagrangian and the generalized -saddle point for Pareto optimality are studied. 相似文献
4.
In the present paper we are concerned with convergence in -density and -statistical convergence of sequences of functions defined on a subset D of real numbers, where is a finitely additive measure. Particularly, we introduce the concepts of -statistical uniform convergence and -statistical pointwise convergence, and observe that -statistical uniform convergence inherits the basic properties of uniform convergence. 相似文献
5.
In this paper we introduce the notion of operator semirings of a -semiring to study -semirings. It is shown that the lattices of all left (right) ideals (two-sided ideals) of a -semiring and its right (respectively left) operator semiring are isomorphic. This has many applications to characterize various -semirings.AMS Subject Classification (2000): 16Y60, 16Y99 相似文献
6.
We consider (,,,)structures of parabolic type on hypersurfaces of dual spaces and study the rank of the affinor . We consider almost contact metric structures of parabolic type of the first kind on hypersurfaces of 4dimensional dual metric space. We study the properties of these structures and give examples of normal, integrable, and Sasakian parabolic structures. 相似文献
7.
K. R. Kazmi 《Journal of Optimization Theory and Applications》2001,109(3):667-674
The -generalized minima for vector optimization problems are defined and a sufficient condition for the existence of -generalized minima for vector optimization problems is established. 相似文献
8.
A -frame is a lattice in which countable joins exist and binary meets distribute over countable joins. In this paper, the category MFrm, of metric -frames, is introduced, and it is shown to be equivalent to the category MLFrm
u, of metric Lindelöf frames.Finally, it is shown that the complete metric -frames are exactly the cozero parts of complete metric Lindelöf frames. 相似文献
9.
The stability of linear timedelay systems with point internal delays is difficult to deal with in practice because of the fact that their characteristic equation is usually of transcendent type rather than of polynomial type. This feature usually causes the system to possess an infinite number of poles. In this paper, stability tests for this class of systems are obtained based either on extensions of classical tests applicable to delayfree systems or on approaches within the framework of twodimensional digital filters. Some of those twodimensional stability tests are also proved to be useful for stability testing of a common class of linear hybrid systems which involve coupled continuous and digital substates after a slightadhoc adaptation of the tests for that situation. 相似文献
10.
Olivier Mazet 《Potential Analysis》2002,16(3):279-287
The positivity of the carré du champ operator is a direct consequence of the positivity of the associated Markov semigroup. We show in this note that the reciprocal implication holds in invariant measure, under minimal hypotheses of continuity and stability. 相似文献
11.
The ordered K0-group of the universal, unital free product C*-algebra Mk()*Ml()is calculated in the case where k is prime and not a divisor in l. It is shown that the positive cone of K0(Mk()*Ml())is as small as possible in this case. The article also contains results (full and partial) on the ordered K00-group of more general universal, unital free product C* algebras. 相似文献
12.
Michael Farber 《K-Theory》1998,15(4):347-405
In this paper we suggest a new general formalism for studying the L2 invariants of polyhedra and manifolds. First, we examine generality in which one may apply the construction of the extended Abelian category, which was earlier suggested by the author using the ideas of P. Freyd. This leads to the notions of a finite von Neumann category and a trace on such a category. Given a finite von Neumann category, we study the extended L2 homology and cohomology theories with values in the Abelian extension. Any trace on the initial category produces numerical invariants – the von Neumann dimension and the Novikov–Shubin numbers. Thus, we obtain the local versions of the Novikov–Shubin invariants, localized at different traces. In the Abelian case this localization can be made more geometric: we show that any torsion object determines a divisor – a closed subspace of the space of the parameters. The divisors of torsion objects together with the information produced by the local Novikov–Shubin invariants may be used to study multiplicities of intersections of algebraic and analytic varieties (we discuss here only simple examples demonstrating this possibility). We compute explicitly the divisors and the von Neumann dimensions of the extended L2 cohomology in the real analytic situation. We also give general formulae for the extended L2 cohomology of a mapping torus. Finally, we show how one can define a De Rham version of the extended cohomology and prove a De Rhamtype theorem. 相似文献
13.
Let R be a ring and M a right R-module. M is called -cofinitely supplemented if every submodule N of M with M/N finitely generated has a supplement that is a direct summand of M. In this paper various properties of the -cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of -cofinitely supplemented modules is -cofinitely supplemented. (2) A ring R is semiperfect if and only if every free R-module is -cofinitely supplemented. In addition, if M has the summand sum property, then M is -cofinitely supplemented iff every maximal submodule has a supplement that is a direct summand of M. 相似文献
14.
We prove the completeness and decidability of the Hornlike sequents, specifically, the socalled D2sequents (of the firstorder linear temporal logic) considered in the author's paper [Lith. Math. J., 41(3), 266–281 (2001)]. In this paper, with the help of the infinitary calculus GL, grounded by the author in his earlier papers, for D2sequents we construct a D2Sat calculus of the socalled saturated type consisting of decidable deductive procedures replacing the omegarule for the always operator. In the present paper, in order to prove the completeness and decidability of the calculus D2Sat, we construct the socalled invariant decidable calculus D2IN. We prove the equivalence of the calculi D2IN, D2Sat, and G
L
**
for the socalled saturated D2sequents. From this equivalence, by reducing an arbitrary D2sequent to a saturated D2sequent, and also from the completeness of the G
L
**
calculus and decidability of the invariant calculus D2IN, we deduce the completeness and decidability of the calculus D2Sat in the class of D2sequents. 相似文献
15.
H. D. Tuan 《Journal of Optimization Theory and Applications》1995,85(2):435-472
LetF:[0, T]×R
n
2
R
n
be a set-valued map with compact values; let :R
n
R
m
be a locally Lipschitzian map,z(t) a given trajectory, andR the reachable set atT of the differential inclusion
. We prove sufficient conditions for (z(T))intR and establish necessary conditions in maximum principle form for (z(T))(R). As a consequence of these results, we show that every boundary trajectory is simultaneously a Pontryagin extremal, Lagrangian extremal, and relaxed Lagrangian extremal.The author is grateful to an anonymous referee for his valuable remarks and comments which have helped to improve the paper.The paper was written while the author was visiting the laboratory of Prof. S. Suzuki, Department of Mechanical Engineering, Sophia University, Tokyo, Japan. 相似文献
16.
In this paper, we consider multipleclass queueing systems with Npolicy in which the idle server starts service as soon as the number of customers in the startup class reaches threshold N. We consider the cases of FCFS and nonpreemptive priority. We obtain the Laplace–Stieltjes transform of the waiting times of each class of customers. We also show some results for the general behavior of such systems. 相似文献
17.
We obtain a more precise asymptotic formula than in [Lith. Math. J., 41(2), 168–177 (2001)] for the mean square of the periodic zetafunction. 相似文献
18.
Tadeusz Antczak 《Journal of Global Optimization》2003,27(4):485-495
In this paper, optimality for multiobjective programming problems having invex objective and constraint functions (with respect to the same function ) is considered. An equivalent vector programming problem is constructed by a modification of the objective function. Furthermore, an -Lagrange function is introduced for a constructed multiobjective problem and modified saddle point results are presented. 相似文献
19.
20.
Z. Q. Han 《Journal of Optimization Theory and Applications》1996,90(2):457-463
This paper establishes a relation between -based cones and solid cones in a separated locally convex topological vector space. The relation reveals that the properties of the base of a based cone affect deeply the topological properties of the dual cone.The author would like to thank Professor C. C. Huang for his discussion on the proof of Corollary 2.1. The author is also grateful to the referees for helpful comments and suggestions. 相似文献