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41.
We perform the dimensional reduction of the linear σ model at one-loop level. The effective potential of the reduced theory obtained from the integration over the nonzero Matsubara frequencies is exhibited. Thermal mass and coupling constant renormalization constants are given, as well as the thermal renormalization group equation which controls the dependence of the counterterms on the temperature. We also recover, for the reduced theory, the vacuum unstability of the model for large N. 相似文献
42.
This paper is devoted to the study of a new necessary condition in variational inequality problems: approximated gradient
projection (AGP). A feasible point satisfies such condition if it is the limit of a sequence of the approximated solutions
of approximations of the variational problem. This condition comes from optimization where the error in the approximated solution
is measured by the projected gradient onto the approximated feasible set, which is obtained from a linearization of the constraints
with slack variables to make the current point feasible.
We state the AGP condition for variational inequality problems and show that it is necessary for a point being a solution
even without constraint qualifications (e.g., Abadie’s). Moreover, the AGP condition is sufficient in convex variational inequalities.
Sufficiency also holds for variational inequalities involving maximal monotone operators subject to the boundedness of the
vectors in the image of the operator (playing the role of the gradients). Since AGP is a condition verified by a sequence,
it is particularly interesting for iterative methods.
Research of R. Gárciga Otero was partially supported by CNPq, FAPERJ/Cientistas do Nosso Estado, and PRONEX Optimization.
Research of B.F. Svaiter was partially supported by CNPq Grants 300755/2005-8 and 475647/2006-8 and by PRONEX Optimization. 相似文献
43.
In this paper a new class of proximal-like algorithms for solving monotone inclusions of the form T(x)∋0 is derived. It is obtained by applying linear multi-step methods (LMM) of numerical integration in order to solve the
differential inclusion , which can be viewed as a generalization of the steepest decent method for a convex function. It is proved that under suitable
conditions on the parameters of the LMM, the generated sequence converges weakly to a point in the solution set T
−1
(0). The LMM is very similar to the classical proximal point algorithm in that both are based on approximately evaluating
the resolvants of T. Consequently, LMM can be used to derive multi-step versions of many of the optimization methods based on the classical proximal
point algorithm. The convergence analysis allows errors in the computation of the iterates, and two different error criteria
are analyzed, namely, the classical scheme with summable errors, and a recently proposed more constructive criterion.
Received: April 2001 / Accepted: November 2002
Published online: February 14, 2003
Key Words. proximal point algorithm – monotone operator – numerical integration – strong stability – relative error criterion
Mathematics Subject Classification (1991): 20E28, 20G40, 20C20 相似文献
44.
Rolando Gárciga Otero B.F. Svaiter 《Journal of Mathematical Analysis and Applications》2004,289(2):700-711
This paper is devoted to the study of strong convergence in inexact proximal like methods for finding zeroes of maximal monotone operators in Banach spaces. Convergence properties of proximal point methods in Banach spaces can be summarized as follows: if the operator have zeroes then the sequence of iterates is bounded and all its weak accumulation points are solutions. Whether or not the whole sequence converges weakly to a solution and which is the relation of the weak limit with the initial iterate are key questions. We present a hybrid proximal Bregman projection method, allowing for inexact solutions of the proximal subproblems, that guarantees strong convergence of the sequence to the closest solution, in the sense of the Bregman distance, to the initial iterate. 相似文献
45.
We exhibit Gödel's geometry in terms of a set of gaussian systems of coordinates, the union of which constitutes a complete cover for the whole manifold. We present a mechanism which induces a particle to follow a closed time-like line (CTL) present in this geometry. We generalize the construction of special class of observers (Generalized Milne Observers) which provides a way to define the largest causal domain allowing a standard field theory to be developed. 相似文献
46.
A family of projective splitting methods for the sum of two maximal monotone operators 总被引:1,自引:0,他引:1
A splitting method for two monotone operators A and B is an algorithm that attempts to converge to a zero of the sum A + B by solving a sequence of subproblems, each of which involves only the operator A, or only the operator B. Prior algorithms of this type can all in essence be categorized into three main classes, the Douglas/Peaceman-Rachford class,
the forward-backward class, and the little-used double-backward class. Through a certain “extended” solution set in a product
space, we construct a fundamentally new class of splitting methods for pairs of general maximal monotone operators in Hilbert
space. Our algorithms are essentially standard projection methods, using splitting decomposition to construct separators.
We prove convergence through Fejér monotonicity techniques, but showing Fejér convergence of a different sequence to a different
set than in earlier splitting methods. Our projective algorithms converge under more general conditions than prior splitting
methods, allowing the proximal parameter to vary from iteration to iteration, and even from operator to operator, while retaining
convergence for essentially arbitrary pairs of operators. The new projective splitting class also contains noteworthy preexisting
methods either as conventional special cases or excluded boundary cases.
Dedicated to Clovis Gonzaga on the occassion of his 60th birthday. 相似文献
47.
Emerson V. Castelani André L. M. Martinez J. M. Martínez B. F. Svaiter 《Computational Optimization and Applications》2010,46(2):229-245
When one solves Nonlinear Programming problems by means of algorithms that use merit criteria combining the objective function
and penalty feasibility terms, a phenomenon called greediness may occur. Unconstrained minimizers attract the iterates at early stages of the calculations and, so, the penalty parameter
needs to grow excessively, in such a way that ill-conditioning harms the overall convergence. In this paper a regularization
approach is suggested to overcome this difficulty. An Augmented Lagrangian method is defined with the addition of a regularization
term that inhibits the possibility that the iterates go far from a reference point. Convergence proofs and numerical examples
are given. 相似文献
48.
49.
A theorem due to Fitzpatrick provides a representation of arbitrary maximal monotone operators by convex functions. This paper explores representability of arbitrary (nonnecessarily maximal) monotone operators by convex functions. In the finite-dimensional case, we identify the class of monotone operators that admit a convex representation as the one consisting of intersections of maximal monotone operators and characterize the monotone operators that have a unique maximal monotone extension.Mathematics Subject Classifications (2000) 47H05, 46B99, 47H17. 相似文献
50.
B. F. Svaiter 《Set-Valued Analysis》2000,8(4):311-328
We introduce a family of enlargements of maximal monotone operators. The Brønsted and Rockafellar -subdifferential operator can be regarded as an enlargement of the subdifferential. The family of enlargements introduced in this paper generalizes the Brønsted and Rockafellar -subdifferential (enlargement) and also generalize the enlargement of an arbitrary maximal monotone operator recently proposed by Burachik, Iusem and Svaiter. We characterize the biggest and the smallest enlargement belonging to this family and discuss some general properties of its members. A subfamily is also studied, namely the subfamily of those enlargements which are also additive. Members of this subfamily are formally closer to the -subdifferential. Existence of maximal elements is proved. In the case of the subdifferential, we prove that the -subdifferential is maximal in this subfamily. 相似文献