Stopping criteria for linesearch methods without derivatives

In this paper acceptability criteria for the linesearch stepsize are introduced which require only function values. Simple algorithm models based on these criteria are presented. Some modifications of criteria based on the knowledge of the directional derivative are also illustrated. This paper was written while this author was visiting CRAI.     

A note on a criterion for M-matrix

The aim of this work is to propose a novel method for confirming whether a given matrix is an M-matrix. The proposed method has the advantage of allowing one to deduce whether the matrix whose entry consists of the functional order is an M-matrix.     

A note on a refined version of Anderson-Brownawell-Papanikolas criterion

We give a refinement of the linear independence criterion over function fields developed by Anderson, Brownawell and Papanikolas [Greg W. Anderson, W. Dale Brownawell, Matthew A. Papanikolas, Determination of the algebraic relations among special Γ-values in positive characteristic, Ann. of Math. 160 (2004) 237-313]. As a consequence, a function field analogue of the Siegel-Shidlovskii theorem is derived.     

A note on quasi-newton formulae for sparse second derivative matrices

In order to apply quasi-Newton methods to solve unconstrained minimization calculations when the number of variables is very large, it is usually necessary to make use of any sparsity in the second derivative matrix of the objective function. Therefore, it is important to extend to the sparse case the updating formulae that occur in variable metric algorithms to revise the estimate of the second derivative matrix. Suitable extensions suggest themselves when the updating formulae are derived by variational methods [1, 3]. The purpose of the present paper is to give a new proof of a theorem of Dennis and Schnabel [1], that shows the effect of sparsity on updating formulae for second derivative estimates.     

A note on the convergence of an algorithm for nonconvex programming problems

A strong convergence theorem is proven to hold for the general algorithm of the branch and bound type for solving nonconvex programming problems given in [1].     

A note on the stability criterion for a class of nonlinear fractional differential systems

This paper is devoted to dealing with a flaw that existed in a recent paper (Zhou et al. 2014). We give a new proof of Th. 3.1 in Zhou et al. (2014), which is a correction of the original proof.     

A note on the allocation of queuing facilities using a minisum criterion

This paper suggests a formulation and a solution procedure for resource allocation problems which consider a central planner, m static queuing facilities providing a homogeneous service at their locations, and a known set of demand points or customers. It is assumed that upon a request for service the customer is routed to a facility by a probabilistic assignment. The objective is to determine how to allocate a limited number of servers to the facilities, and to specify demand rates from customers to facilities in order to minimize a weighted sum of response times. This sum measures the total time lost in the system due to two sources: travel time from customer to facility locations and waiting time for service at the facilities. The setting does not allow for cooperation between the facilities.     

A note on algebraic independence criterion for Laurent series in positive characteristic

Periodica Mathematica Hungarica - We study the algebraic independence of Laurent series in positive characteristic which can be fast approximated by rational functions. This can be seen as a...     

A note on selection of proposers in coalitional bargaining

This paper presents a noncooperative coalitional bargaining model with a generalized selection of proposers, which includes two frequently used selection protocols, i.e., the fixed-order-proposer protocol and the random-proposer protocol. In the model, proposers are selected in each bargaining round according to recognition probabilities contingent on the identity of the rejector in the preceding round. This paper provides an equivalent condition for the existence of an efficient equilibrium for each discount factor. It is shown that for each discount factor, the possibility of the existence of an efficient equilibrium decreases as the probability that the rejector in the preceding round becomes a proposer increases. This paper is a revised version of Kawamori (2006). The author is grateful to the editor, William Thomson, the associate editor, an anonymous referee, Hiroaki Ino, Minoru Kitahara, Toshihiro Matsumura, Toshiji Miyakawa, Akira Okada, Masahiro Okuno-Fujiwara, Dan Sasaki, Tadashi Sekiguchi, Kazuo Yamaguchi, and the seminar participants at the 2006 Spring Meeting of the Japanese Economic Association for their valuable comments and suggestions. The author gratefully acknowledges the Japan Society for the Promotion of Science (JSPS) Research Fellowship for Young Scientists and the Grant-in-Aid for JSPS Fellows.     

A bayes procedure for selecting the population with the largestpth quantile

Summary The Bayes method is seldom applied to nonparametric statistical problems, for the reason that it is hard to find mathematically tractable prior distributions on a set of probability measures. However, it is found that the Dirichlet process generates randomly a family of probability distributions which can be taken as a family of prior distributions for an application of the Bayes method to such problems. This paper presents a Bayesian analysis of a nonparametric problem of selecting a distribution with the largestpth quantile value, fromk≧2 given distributions. It is assumed a priori that the given distributions have been generated from a Dirichlet process. This work was supported by the U.S. Office of Naval Research under Contract No. 00014-75-C-0451.     

A note on the de La Vallée Poussin criterion for uniform integrability

In this paper, we present new versions of the classical de La Vallée Poussin criterion for uniform integrability. Our results concern the uniform integrability of a continuous function relative to a sequence of distribution functions. We apply our results to obtain a result on the convergence of a sequence of integrals which we illustrate with an example.     

A note on solving nonlinear equations and the natural criterion function

We consider the natural criterion function for controlling a damped Newton iteration used for solving systems of nonlinear equations. An example is given which shows that the method can cycle in an undesirable manner, not possible when using the more conventional least-squares criterion function. Despite this, the natural criterion function is of value in particular applications. This point is illustrated using a system derived from a nonlinear two-point boundary-value problem.     

A note on the efficient implementation of Hamiltonian BVMs

We discuss the efficient implementation of Hamiltonian BVMs (HBVMs), a recently introduced class of energy preserving methods for canonical Hamiltonian systems (see Brugnano et al. [8] and references therein), also sketching their blended formulation. We also discuss the case of separable problems, for which the structure of the problem can be exploited to gain efficiency.     

Experiments with a new selection criterion in a fast interval optimization algorithm

Usually, interval global optimization algorithms use local search methods to obtain a good upper (lower) bound of the solution. These local methods are based on point evaluations. This paper investigates a new local search method based on interval analysis information and on a new selection criterion to direct the search. When this new method is used alone, the guarantee to obtain a global solution is lost. To maintain this guarantee, the new local search method can be incorporated to a standard interval GO algorithm, not only to find a good upper bound of the solution, but also to simultaneously carry out part of the work of the interval B&B algorithm. Moreover, the new method permits improvement of the guaranteed upper bound of the solution with the memory requirements established by the user. Thus, the user can avoid the possible memory problems arising in interval GO algorithms, mainly when derivative information is not used. The chance of reaching the global solution with this algorithm may depend on the established memory limitations. The algorithm has been evaluated numerically using a wide set of test functions which includes easy and hard problems. The numerical results show that it is possible to obtain accurate solutions for all the easy functions and also for the investigated hard problems.     

A new linesearch algorithm for nonlinear least squares problems

A linesearch (steplength) algorithm for unconstrained nonlinear least squares problems is described. To estimate the steplength inside the linesearch algorithm a new method that interpolates the residual vector is used together with a standards method that interpolates the sums of squares. Numerical results are reported that point out the advantage with the new steplength estimation method.     

A relaxation algorithm for the minimization of a quasiconcave function on a convex polyhedron

A study was made of the global minimization of a general quasiconcave function on a convex polyhedron. This nonconvex problem arises in economies of scale environments and in alternative formulations of other well-known problems, as in the case of bilinear programming.Although not very important in our final results, a local minimum can be easily obtained. However, a major aspect is the existence of two families of lower bounds on the optimal functional value: one is provided by non-linear programming duality, the other is derived from a lexicographic ordering of basic solutions which allows the use of relaxation concepts. These results were exploited in a finite algorithm for obtaining the global minimum whose initial implementation has had encouraging performance.