benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

extremal hexagonal chains with respect to the coefficients sum of the permanental polynomial a hexagonal system is a graphical representation of a benzenoid hydrocarbon in theoretical chemistry a hexagonal chain is a cata condensed hexagonal system with no branchings in this paper we consider extremal hexagonal chains with respect to the coefficients sum of the permanental polynomial we prove that the linear chain attains the minimum value of this sum and the zigzag chain attains the maximum value of this sum

a solution to the problem of rasa connected with bernstein polynomials abstract during the conference on ulam s type stability rytro poland 2014 ioan rasa recalled his 25 years old problem concerning some inequality involving the bernstein polynomials we offer the complete solution in positive as a tool we use stochastic orderings which we prove for binomial distributions as well as so called concentration inequality our methods allow us to pose and solve the extended version of the problem in question

on the greatest distance between two permanental roots of a matrix abstract the permanental spread of a complex square matrix a is defined to be the greatest distance between two roots of the equation per zi a 0 a preliminary study of this number as well as of two related quantities is given in particular we derive upper and lower bounds and deal with comparisons of different bounds finally two inequalities involving the permanental spread are treated

a nonlinear conjugate gradient method with a strong global convergence property conjugate gradient methods are widely used for unconstrained optimization especially large scale problems the strong wolfe conditions are usually used in the analyses and implementations of conjugate gradient methods this paper presents a new version of the conjugate gradient method which converges globally provided the line search satisfies the standard wolfe conditions the conditions on the objective function are also weak being similar to those required by the zoutendijk condition

on the characterizing properties of the permanental polynomials of graphs abstract let g be a graph and a g the adjacency matrix of g the permanental polynomial of g is defined as g x per x i a g if two graphs g and h have the same permanental polynomial then g is called a per cospectral mate of h a graph g is said to be characterized by its permanental polynomial if all the per cospectral mates of g are isomorphic to g it is shown that complete graphs stars regular complete bipartite graphs and odd cycles are characterized by their permanental polynomials we prove that in general the permanental polynomial cannot characterize the paths and even cycles in particular for each l 1 and m 2 we can find non isomorphic per cospectral mates of p 4 l 3 and c 4 m respectively when we restrict our consideration to connected graphs both the paths and even cycles c 4 l 2 are characterized by their permanental polynomials

new accelerated conjugate gradient algorithms as a modification of dai yuan s computational scheme for unconstrained optimization new accelerated nonlinear conjugate gradient algorithms which are mainly modifications of dai and yuan s for unconstrained optimization are proposed using the exact line search the algorithm reduces to the dai and yuan conjugate gradient computational scheme for inexact line search the algorithm satisfies the sufficient descent condition since the step lengths in conjugate gradient algorithms may differ from 1 by two orders of magnitude and tend to vary in a very unpredictable manner the algorithms are equipped with an acceleration scheme able to improve the efficiency of the algorithms computational results for a set consisting of 750 unconstrained optimization test problems show that these new conjugate gradient algorithms substantially outperform the dai yuan conjugate gradient algorithm and its hybrid variants hestenes stiefel polak ribiere polyak conmin conjugate gradient algorithms limited quasi newton algorithm lbfgs and compare favorably with cg descent in the frame of this numerical study the accelerated scaled memoryless bfgs preconditioned conjugate gradient ascalcg algorithm proved to be more robust

permanental polynomials of graphs abstract the first section surveys recent results on the permanental polynomial of a square matrix a i e per xi a the second section concerns the permanental polynomial of the adjacency matrix of a graph the final section is an introduction to the permanental polynomial of the laplacian matrix of a graph an appendix lists some of these latter polynomials

polyhedral object recognition by indexing in computer vision the indexing problem is the problem of recognizing a few objects in a large database of objects while avoiding the help of the classical image feature to object feature matching paradigm in this paper we address the problem of recognizing three dimensional 3 d polyhedral objects from 2 d images by indexing both the objects to be recognized and the images are represented by weighted graphs the indexing problem is therefore the problem of determining whether a graph extracted from the image is present or absent in a database of model graphs we introduce a novel method for performing this graph indexing process which is based both on polynomial characterization of binary and weighted graphs and on hashing we describe in detail this polynomial characterization and then we show how it can be used in the context of polyhedral object recognition next we describe a practical recognition by indexing system that includes the organization of the database the representation of polyhedral objects in terms of 2 d characteristic views the representation of this views in terms of weighted graphs and the associated image processing finally some experimental results allow the evaluation of the system performance

a new class of nonlinear conjugate gradient coefficients with global convergence properties abstract nonlinear conjugate gradient cg methods have played an important role in solving large scale unconstrained optimization their wide application in many fields is due to their low memory requirements and global convergence properties numerous studies and modifications have been conducted recently to improve this method in this paper a new class of conjugate gradient coefficients k that possess global convergence properties is presented the global convergence result is established using exact line searches numerical result shows that the proposed formula is superior and more efficient when compared to other cg coefficients

new conjugacy condition and related new conjugate gradient methods for unconstrained optimization the conjugate gradient cg method has played a special role in solving large scale nonlinear optimization due to the simplicity of their iterations and their very low memory requirements based on a new quasi newton equation proposed in z wei g li l qi new quasi newton methods for unconstrain optimization preprint z wei g yu g yuan z lian the superlinear convergence of a modified bfgs type method for unconstrained optimization comput optim appl 29 3 2004 315 332 we establish a new conjugacy condition for cg methods and propose several new cg methods it is a interesting feature that these new cg methods take both the gradient and function value information under some suitable conditions the global convergence is achieved for these methods the numerical results show that one of our new cg methods is very encouraging

on markov operators preserving polynomials abstract the paper is concerned with a special class of positive linear operators acting on the space c k of all continuous functions defined on a convex compact subset k of r d d 1 having non empty interior actually this class consists of all positive linear operators t on c k which leave invariant the polynomials of degree at most 1 and which in addition map polynomials into polynomials of the same degree among other things we discuss the existence of such operators in the special case where k is strictly convex by also characterizing them within the class of positive projections in particular we show that such operators exist if and only if k is an ellipsoid furthermore a characterization of balls of r d in terms of a special class of them is furnished additional results and illustrative examples are presented as well

on the limited memory bfgs method for large scale optimization we study the numerical performance of a limited memory quasi newton method for large scale optimization which we call the l bfgs method we compare its performance with that of the method developed by buckley and lenir 1985 which combines cycles of bfgs steps and conjugate direction steps our numerical tests indicate that the l bfgs method is faster than the method of buckley and lenir and is better able to use additional storage to accelerate convergence we show that the l bfgs method can be greatly accelerated by means of a simple scaling we then compare the l bfgs method with the partitioned quasi newton method of griewank and toint 1982a the results show that for some problems the partitioned quasi newton method is clearly superior to the l bfgs method however we find that for other problems the l bfgs method is very competitive due to its low iteration cost we also study the convergence properties of the l bfgs method and prove global convergence on uniformly convex problems

on the geometry and laplacian of a graph abstract let g be a simple graph on n vertices and let l be the laplacian matrix of g we point out some connections between the geometric properties of g and the spectrum of l the multiplicities and eigenspaces as well as the eigenvalues of l are of geometric interest some historical information and relations of l to other matrices associated with g are also described

a new class of nonlinear conjugate gradient coefficients with exact and inexact line searches conjugate gradient cg methods have played an important role in solving large scale unconstrained optimization in this paper we propose a new family of cg coefficients k that possess sufficient descent conditions and global convergence properties this new k is an extension of the already proven k rmil from rivaie et al 19 a new class of nonlinear conjugate gradient coefficient with global convergence properties appl math comp 218 2012 11323 11332 global convergence result is established using both exact and inexact line searches numerical results show that the performance of the new proposed formula is quite similar to k rmil and suited to both line searches importantly the performance of this k is more efficient and superior than the other well known k

immanantal invariants of graphs abstract something between an expository note and an extended research problem this article is an invitation to expand the existing literature on a family of graph invariants rooted in linear and multilinear algebra there are a variety of ways to assign a real n n matrix k g to each n vertex graph g so that g and h are isomorphic if and only if k g and k h are permutation similar it follows that g and h are isomorphic only if k g and k h are similar i e that similarity invariants of k g are graph theoretic invariants of g an observation that helps to explain the enormous literature on spectral graph theory the focus of this article is the permutation part i e on matrix functions that are preserved under permutation similarity if not under all similarity

convergence properties of nonlinear conjugate gradient methods recently important contributions on convergence studies of conjugate gradient methods were made by gilbert and nocedal siam j optim 2 1992 pp 21 42 they introduce a sufficient descent condition to establish global convergence results although this condition is not needed in the convergence analyses of newton and quasi newton methods gilbert and nocedal hint that the sufficient descent condition which was enforced by their two stage line search algorithm may be crucial for ensuring the global convergence of conjugate gradient methods this paper shows that the sufficient descent condition is actually not needed in the convergence analyses of conjugate gradient methods consequently convergence results on the fletcher reeves and polak ribiere type methods are established in the absence of the sufficient descent condition to show the differences between the convergence properties of fletcher reeves and polak ribiere type methods two examples are constructed showing that neither the boundedness of the level set nor the restriction beta k geq 0 can be relaxed for the polak ribiere type methods

learning graphical model parameters with approximate marginal inference likelihood based learning of graphical models faces challenges of computational complexity and robustness to model misspecification this paper studies methods that fit parameters directly to maximize a measure of the accuracy of predicted marginals taking into account both model and inference approximations at training time experiments on imaging problems suggest marginalization based learning performs better than likelihood based approximations on difficult problems where the model being fit is approximate in nature

on the permanental sum of graphs abstract let g be a graph and a g the adjacency matrix of g the polynomial g x per x i a g is called the permanental polynomial of g and the permanental sum of g is the summation of the absolute values of the coefficients of g x in this paper we investigate properties of permanental sum of a graph prove recursive formulas to compute the permanental sum of a graph and show that the ordering of graphs with respect to permanental sum furthermore we determine the upper and lower bounds of permanental sum of unicyclic graphs and the corresponding extremal unicyclic graphs are also determined

on the bivariate permanent polynomials of graphs abstract in 1980 balasubramanian and parthasarathy introduced the bivariate permanent polynomials of graphs and conjectured that this polynomial is a graph characterizing polynomial that is any two graphs with the same bivariate permanent polynomial are isomorphic in this paper we give counterexamples to this conjecture by a computer search furthermore we show that several well known families of graphs are determined by the bivariate permanent polynomial complete graphs complete bipartite graphs regular complete multipartite graphs cycles and their complements

a bound for the permanent of the laplacian matrix abstract it is shown that if g is a simple connected graph on n vertices then per l g 2 n 1 g where l g is the laplacian matrix of g and g is the complexity of g

regularity properties of semigroups generated by some fleming viot type operators abstract we study different qualitative properties of the semigroup generated by some degenerate differential elliptic operators on the standard simplex of r d some methods are new and are based on the representation formulas of the semigroup in terms of iterates of suitable positive operators the main result is the ultracontractivity property which is obtained in the setting of weighted l p spaces we describe the asymptotic behavior of the semigroup and obtain the compactness property in the same setting and also in spaces of continuous functions

per spectral characterizations of graphs with extremal per nullity abstract a graph g is said to be determined by its permanental spectrum if any graph having the same permanental spectrum as g is isomorphic to g in this paper we introduce the permanental nullity of a graph the multiplicity of the number zero in the permanental spectrum of a graph to study graphs determined by their permanental spectra first we determine all graphs of order n whose permanental nullities are n 2 n 3 n 4 and n 5 respectively then we show that all graphs with the permanental nullity n 2 n 3 or n 5 and all non bipartite graphs with the permanental nullity n 4 are determined by their permanental spectra in particular we prove that the complete bipartite graphs are determined by their permanental spectra

computing the permanental polynomials of graphs let m be an nn matrix with entries mij i j 1 2 n the permanent of m is defined to be per m i 1nmi i where the sum is taken over all permutations of 1 2 n the permanental polynomial of m is defined by per xinm where in is the identity matrix of size n in this paper we give recursive formulas for computing permanental polynomials of the laplacian matrix and the signless laplacian matrix of a graph respectively

a note on the global convergence theorem of accelerated adaptive perry conjugate gradient methods abstract in andrei 2017 a class of efficient conjugate gradient algorithms acgssv is proposed for solving large scale unconstrained optimization problems however due to a wrong inequality and an incorrect reasoning used in analyzing the global convergence property for the proposed algorithm the proof of theorem 4 2 the global convergence theorem is incorrect in this paper the necessary corrections are made under common assumptions it is shown that algorithm acgssv converges linearly to the unique minimizer

unicyclic graphs with second largest and second smallest permanental sums abstract let a g be an adjacency matrix of a graph g then the polynomial g x per x i a g is called the permanental polynomial of g and the permanental sum of g is the sum of the absolute values of the coefficients of g x in this paper the second largest and second smallest permanental sums among connected unicyclic graphs and the corresponding extremal graphs are determined in addition we show that the computation of permanental sum is p complete

permanental roots and the star degree of a graph abstract for undirected graphs without loops or multiple edges we define the star degree of a graph and prove that it is equal to the multiplicity of the root 1 of per xi b where b d a considering bipartite graphs we prove that per xi b per xi l where l d a and consequently that the star degree of a bipartite graph can also be characterized by the multiplicity of the root 1 of per xi l

multiplicity of integer roots of polynomials of graphs abstract let g be a graph with minimum vertex degree p 1 let b d a where d is the diagonal matrix of vertex degrees and a is the adjacency matrix of g the multiplicity of the integer root p of per xi b is characterized for bipartite graphs this characterization extends to per xi l where l d a is the laplacian matrix of g for graphs with unrestricted vertex degrees bounds are obtained on the multiplicities of integer roots of the permanental and characteristic polynomials of both l and b

on differential operators associated with markov operators abstract in this paper we introduce and study a new class of elliptic second order differential operators on a convex compact subset k of r d d 1 which are associated with a markov operator t on c k and which degenerate on a suitable subset of k containing its extreme points among other things we show that the closures of these operators generate markov semigroups moreover we prove that these semigroups can be approximated by means of iterates of suitable positive linear operators which are referred to as the bernstein schnabl operators associated with t as a consequence we show that the semigroups preserve polynomials of a given degree as well as holder continuity which gives rise to some spatial regularity properties of the solutions of the relevant evolution equations

elliptic differential operators and positive semigroups associated with generalized kantorovich operators abstract deepening the study of a new approximation sequence of positive linear operators we introduced and studied in 12 in this paper we disclose its relationship with the markov semigroup pre generation problem for a class of degenerate second order elliptic differential operators which naturally arise through an asymptotic formula as well as with the approximation of the relevant markov semigroups in terms of the approximating operators themselves the analysis is carried out in the context of the space c k of all continuous functions defined on an arbitrary convex compact subset k of r d d 1 having non empty interior and a not necessarily smooth boundary as well as in some particular cases in l p k spaces 1 p the approximation formula also allows to infer some preservation properties of the semigroup such as the preservation of the lipschitz continuity as well as of the convexity we finally apply the main results to some noteworthy particular settings such as balls and ellipsoids the unit interval and multidimensional hypercubes and simplices in these settings the relevant differential operators fall into the class of fleming viot operators

accelerated conjugate gradient algorithm with finite difference hessian vector product approximation for unconstrained optimization in this paper we propose a fundamentally different conjugate gradient method in which the well known parameter b k is computed by an approximation of the hessian vector product through finite differences for search direction computation the method uses a forward difference approximation to the hessian vector product in combination with a careful choice of the finite difference interval for the step length computation we suggest an acceleration scheme able to improve the efficiency of the algorithm under common assumptions the method is proved to be globally convergent it is shown that for uniformly convex functions the convergence of the accelerated algorithm is still linear but the reduction in function values is significantly improved numerical comparisons with conjugate gradient algorithms including conmin by shanno and phua d f shanno k h phua algorithm 500 minimization of unconstrained multivariate functions acm trans math softw 2 1976 87 94 scalcg by andrei n andrei scaled conjugate gradient algorithms for unconstrained optimization comput optim appl 38 2007 401 416 n andrei scaled memoryless bfgs preconditioned conjugate gradient algorithm for unconstrained optimization optim methods softw 22 2007 561 571 n andrei a scaled bfgs preconditioned conjugate gradient algorithm for unconstrained optimization appl math lett 20 2007 645 650 and new conjugacy condition and related new conjugate gradient by li tang and wei g li c tang z wei new conjugacy condition and related new conjugate gradient methods for unconstrained optimization j comput appl math 202 2007 523 539 or truncated newton tn by nash s g nash preconditioning of truncated newton methods siam j on scientific and statistical computing 6 1985 599 616 using a set of 750 unconstrained optimization test problems show that the suggested algorithm outperforms these conjugate gradient algorithms as well as tn

highly unique network descriptors based on the roots of the permanental polynomial in this paper we examine the zeros of permanental polynomials as highly unique network descriptors we employ exhaustively generated networks and demonstrate that our defined graph measures based on the moduli of the zeros of permanental polynomials are quite efficient when distinguishing graphs structurally in this work we continue with a line of research that relates to the search of almost complete graph invariants these highly unique network measures may serve as a powerful tool for tackling graph isomorphism