Berinde has shown that Newton’s method for a scalar equation f (x) = 0 converges under some conditions involving only f and f ′ and not f ′′ when a generalized stopping inequality is valid. Later Sen et al. have extended Berinde’s theorem to the case where the condition that f ′(x) = 0 need not necessarily be true. In this paper we have extended Berinde’s theorem to the class of n-dimensional e...

The complexity of finding ǫ-approximate first-order critical points for the general smooth constrained optimization problem is shown to be no worse that O(ǫ) in terms of function and constraints evaluations. This result is obtained by analyzing the worst-case behaviour of a first-order shorts-step homotopy algorithm consisting of a feasibility phase followed by an optimization phase, and requir...

The Heisenberg inequality ∆X∆P ≥ h̄/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The significance of this “exact” uncertainty relation is discussed, and results are generalised to angular momentum and phase, photon number and phase, time and frequency, and to states described by density operators....

The mixture model likelihood function is invariant with respect to permutation of the components of the mixture. If functions of interest are permutation sensitive, as in classification applications, then interpretation of the likelihood function requires valid inequality constraints and a very large sample may be required to resolve ambiguities. If functions of interest are permutation invaria...

We introduce a new class of lower bounds on the log partition function of a Markov random field which makes use of a reversed Jensen’s inequality. In particular, our method approximates the intractable distribution using a linear combination of spanning trees with negative weights. This technique is a lower-bound counterpart to the tree-reweighted belief propagation algorithm, which uses a conv...

The Heisenberg inequality ∆X∆P ≥ h̄/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The significance of this “exact” uncertainty relation is discussed, and results are generalised to angular momentum and phase, photon number and phase, time and frequency, and to states described by density operators....

Let L be a family of lattice-free polyhedra in R containing the splits. Given a polyhedron P in R, we characterize when a valid inequality for P ∩(Z×R) can be obtained with a finite number of disjunctive cuts corresponding to the polyhedra in L. We also characterize the lattice-free polyhedra M such that all the disjunctive cuts corresponding to M can be obtained with a finite number of disjunc...

The motivation of this work is to illustrate the efficiency of some often overlooked alternatives to deal with optimization problems in systems and control. In particular, we will consider a problem for which an iterative linear matrix inequality algorithm (ILMI) has been proposed recently. As it often happens, this algorithm does not have guaranteed global convergence and therefore many method...

Sociologists of (e)valuation have devoted considerable attention to understanding differences in evaluative practices across a number of fields. Yet, little is understood about how individuals learn about and navigate multivalent valid group styles within a single setting. As a social phenomenon, many accept how central processes of evaluation are to everyday life. Accordingly, scholars have at...

This file contains a revised version of the proofs Theorems 3 and 4 paper [1]. In particular, more correct argument is employed to obtain inequality (A11) from (A10), provided that stronger hypothesis on sequence $$\{\varepsilon _k\}$$ included. The practical implementation algorithm (Section 3) remains as it all numerical experiments 4) are still valid since was already satisfied by selected s...