1,721,009 research outputs found
The importance of Perron-Frobenius Theorem in ranking problems
Full text linkThe problem of ranking a set of elements, namely giving a ``rank'' to the elements of the set, may be tackled in many different ways.
In particular a mathematically based ranking scheme can be used and sometimes it may be interesting to see how different can be the results of a mathematically based method compared with some more heuristic ways.
In this working paper some remarks are presented about the importance, in a mathematical approach to ranking schemes, of a classical result from Linear Algebra, the Perron--Frobenius theorem.
To give a motivation of such an importance two different contexts are taken into account, where a ranking problem arises: the example of ranking football/soccer teams and the one of ranking webpages in the approach proposed and implemented by Google's PageRank algorithm
A gradient-like method for quasidifferentiable optimization
No full textFor the minimization of nonsmooth quasidifferentiable functions methods have been defined which make use of a particular structure of the function itself. This usually takes to the knowledge that the quasidifferential is a convex hull of a finite set of gradients and then stopping optimality conditions are sure to be working. In this paper a method for minimizing
a general quasidifferentiable function is presented which do not assume that the objective function has any particular structure apart to be quasidifferentiable. A finite set of computed directional derivatives are used to get an approximation of the quasidifferential. The test of optimality condition and the search for a direction of descent are implemented as the solution of convenient subproblems
A mapping associated to a quadratic optimization problem with linear constraints
No full textIn this working paper we go on with the study of a mapping in Rn associated to a quadratic optimization problem with one equality linear constraint. After showing some general properties related to homogeneity and the inverse mapping, we present some results regarding how the mapping behaves with norms of
vectors. Then some aspects related either to invariant points or invariant subspaces are investigated
Some notes on divisibility rules
No full textA divisibility rule is a shorthand way of determining whether a given number is divisible by a fixed divisor without performing the division, usually by performing a simple calculation on its digits. There is no similarity among these rules, in the sense that for example the rule for testing the divisibility by 3 is very different from the rule for 7.
In this working paper we present a general rule for testing divisibility by two digit integer numbers. The general rule is characterized by a pair of conditions, but in some cases just the main condition of the two is necessary and sufficient for divisibility. In the second part we investigate on this aspect and we show in general what are the cases in which just one condition is enough. Although there are divisibility tests for numbers in any base, and they are usually different, in this paper we concentrate just on the base 10
Performance of a nonsmooth minimization method based on the monotone generalized derivative
No full text
- …
