calculating some inverse linear programming problems in this paper we consider some inverse lp problems in which we need to adjust the cost coefficients of a given lp problem as less as possible so that a known feasible solution becomes the optimal one a method for solving general inverse lp problem including upper and lower bound constraints is suggested which is based on the optimality conditions for lp problems it is found that when the method is applied to inverse minimum cost flow problem or inverse assignment problem we are able to obtain strongly polynomial algorithms

a smoothing newton method for a type of inverse semi definite quadratic programming problem we consider an inverse problem arising from the semi definite quadratic programming sdqp problem we represent this problem as a cone constrained minimization problem and its dual denoted isdqd is a semismoothly differentiable sc 1 convex programming problem with fewer variables than the original one the karush kuhn tucker conditions of the dual problem isdqd can be formulated as a system of semismooth equations which involves the projection onto the cone of positive semi definite matrices a smoothing newton method is given for getting a karush kuhn tucker point of isdqd the proposed method needs to compute the directional derivative of the smoothing projector at the corresponding point and to solve one linear system per iteration the quadratic convergence of the smoothing newton method is proved under a suitable condition numerical experiments are reported to show that the smoothing newton method is very effective for solving this type of inverse quadratic programming problems

partially regular solution to landau lifshitz maxwell equations in two dimensions abstract the present paper is concerned with the existence uniqueness and singularities of the landau lifshitz equation coupled with maxwell equations on riemannian manifold in two dimensions it is shown that there exists a weak solution which is regular with exception of at most finitely many singular points

a penalty function method for solving inverse optimal value problem in order to consider the inverse optimal value problem under more general conditions we transform the inverse optimal value problem into a corresponding nonlinear bilevel programming problem equivalently using the kuhn tucker optimality condition of the lower level problem we transform the nonlinear bilevel programming into a normal nonlinear programming the complementary and slackness condition of the lower level problem is appended to the upper level objective with a penalty then we give via an exact penalty method an existence theorem of solutions and propose an algorithm for the inverse optimal value problem also analysis the convergence of the proposed algorithm the numerical result shows that the algorithm can solve a wider class of inverse optimal value problem

performance of modularity maximization in practical contexts although widely used in practice the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts here we present a broad characterization of its performance in such situations first we revisit and clarify the resolution limit phenomenon for modularity maximization second we show that the modularity function q exhibits extreme degeneracies it typically admits an exponential number of distinct high scoring solutions and typically lacks a clear global maximum third we derive the limiting behavior of the maximum modularity q max for one model of infinitely modular networks showing that it depends strongly both on the size of the network and on the number of modules it contains finally using three real world metabolic networks as examples we show that the degenerate solutions can fundamentally disagree on many but not all partition properties such as the composition of the largest modules and the distribution of module sizes these results imply that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts they also explain why many heuristics are often successful at finding high scoring partitions in practice and why different heuristics can disagree on the modular structure of the same network we conclude by discussing avenues for mitigating some of these behaviors such as combining information from many degenerate solutions or using generative models

maximal flow through a domain in place of flows on a discrete network we study flows described by a vector field x y in a plane domain the analogue of the capacity constraint is c x y and the strength of sources and sinks is n f on the boundary and div f in the interior we show that the largest the maximal flow is determined by the minimal cut as in the discrete case the dual problem has a 0 1 solution given by the characteristic function of the minimal cut for the continuous problem the argument depends on the coarea formula for functions of bounded variation

inverse semidefinite quadratic programming problem with l1 norm measure abstract we consider an inverse problem arising from a semidefinite quadratic programming sdqp problem which is a minimization problem involving l 1 vector norm with positive semidefinite cone constraint by using convex optimization theory the first order optimality condition of the problem can be formulated as a semismooth equation under two assumptions we prove that any element of the generalized jacobian of the equation at its solution is nonsingular based on this a smoothing approximation operator is given and a smoothing newton method is proposed for solving the solution of the semismooth equation we need to compute the directional derivative of the smoothing operator at the corresponding point and to solve one linear system per iteration in the newton method and its global convergence is demonstrated finally we give the numerical results to show the effectiveness and stability of the smoothing newton method for this inverse problem

a projected newton method for l p norm location problems this paper is concerned with the numerical solution of continuous minisum multifacility location problems involving thel p norm where 1 p x this class of problems is potentially difficult to solve because the objective function is not everywhere diflerentiable after developing conditions that characterize the minimum of the problems under consideration a second order algorithm is presented this algorithm is based on the solution of a finite sequence of linearly constrained subproblems descent directions for these subproblems are obtained by projecting the newton direction onto the corresponding constraint manifold univariate minimization is achieved via a specialized linesearch which recognizes the possibility of first derivative discontinuity and second derivative unboundedness at points along the search direction the algorithm motivated by earlier works of calamai and conn and related to methods recently described by overton and dax is shown to possess both global and quadratic convergence properties degeneracy can complicate the numerical solution of the subproblems this degeneracy is identified and a method for handling it is outlined an implementation of the algorithm that exploits the intrinsic structure of the location problem formulation is then described along with a discussion of numerical results

on the complexity of computing the k restricted edge connectivity of a graph the k restricted edge connectivity of a graph g denoted by k g is defined as the minimum size of an edge set whose removal leaves exactly two connected components each containing at least k vertices this graph invariant which can be seen as a generalization of a minimum edge cut has been extensively studied from a combinatorial point of view however very little is known about the complexity of computing k g very recently in the parameterized complexity community the notion of good edge separation of a graph has been defined which happens to be essentially the same as the k restricted edge connectivity motivated by the relevance of this invariant from both combinatorial and algorithmic points of view in this article we initiate a systematic study of its computational complexity with special emphasis on its parameterized complexity for several choices of the parameters we provide a number of np hardness and w 1 hardness results as well as fpt algorithms

symmetric submodular system contractions and gomory hu tree abstract let s v f be a symmetric submodular system for two distinct elements s and l of v let s l denote the set of all subsets of v which separate s from l by using any gomory hu tree of s we can obtain an element of s l which has minimum value among all the elements of s l this tree can be constructed iteratively by solving v 1 minimum s l separator problem pendant pairs of a symmetric submodular system play a key role in finding a minimizer of this system in this paper we obtain a gomory hu tree of a contraction of s with respect to some subsets of v only by using contraction in a gomory hu tree of s furthermore we obtain some pendant pairs of s and of its contractions by using a gomory hu tree of s

on an instance of the inverse shortest paths problem the inverse shortest paths problem in a graph is considered that is the problem of recovering the arc costs given some information about the shortest paths in the graph the problem is first motivated by some practical examples arising from applications an algorithm based on the goldfarb idnani method for convex quadratic programming is then proposed and analyzed for one of the instances of the problem preliminary numerical results are reported

facility location problems in the plane based on reverse nearest neighbor queries for a finite set of points s the monochromatic reverse nearest neighbor rnn rule associates with any query point q the subset of points in s that have q as its nearest neighbor in the bichromatic reverse nearest neighbor brnn rule sets of red and blue points are given and any blue query is associated with the subset of red points that have it as its nearest blue neighbor in this paper we introduce and study new optimization problems in the plane based on the bichromatic reverse nearest neighbor brnn rule we provide efficient algorithms to compute a new blue point under criteria such as 1 the number of associated red points is maximum maxcov criterion 2 the maximum distance to the associated red points is minimum minmax criterion 3 the minimum distance to the associated red points is maximum maxmin criterion these problems arise in the competitive location area where competing facilities are established our solutions use techniques from computational geometry such as the concept of depth of an arrangement of disks or upper envelope of surface patches in three dimensions

globally minimal surfaces by continuous maximal flows in this paper we address the computation of globally minimal curves and surfaces for image segmentation and stereo reconstruction we present a solution simulating a continuous maximal flow by a novel system of partial differential equations existing methods are either grid biased graph based methods or suboptimal active contours and surfaces the solution simulates the flow of an ideal fluid with isotropic velocity constraints velocity constraints are defined by a metric derived from image data an auxiliary potential function is introduced to create a system of partial differential equations it is proven that the algorithm produces a globally maximal continuous flow at convergence and that the globally minimal surface may be obtained trivially from the auxiliary potential the bias of minimal surface methods toward small objects is also addressed an efficient implementation is given for the flow simulation the globally minimal surface algorithm is applied to segmentation in 2d and 3d as well as to stereo matching results in 2d agree with an existing minimal contour algorithm for planar images results in 3d segmentation and stereo matching demonstrate that the new algorithm is robust and free from grid bias

partial regularity to the landau lifshitz equation with spin accumulation abstract in this paper we consider a model for the spin magnetization system that takes into account the diffusion process of the spin accumulation this model consists of the landau lifshitz equation describing the precession of the magnetization coupled with a quasi linear parabolic equation describing the diffusion of the spin accumulation this paper establishes the global existence and uniqueness of weak solutions for large initial data in r 2 moreover partial regularity is shown in particular the solution is regular on r 2 0 with the exception of at most finite singular points

hierarchical inference of unicast network topologies based on end to end measurements in this paper we address the problem of topology discovery in unicast logical tree networks using end to end measurements without any cooperation from the internal routers topology estimation can be formulated as hierarchical clustering of the leaf nodes based on pairwise correlations as similarity metrics unlike previous work that first assumes the network topology is a binary tree and then tries to generalize to a nonbinary tree we provide a framework that directly deals with general logical tree topologies a hierarchical algorithm to estimate the topology is developed in a recursive manner by finding the best partitions of the leaf nodes level by level our simulations show that the algorithm is more robust than binary tree based methods

weight reduction problems with certain bottleneck objectives abstract this paper is concerned with bottleneck weight reduction problems wrps stated as follows we are given a finite set e a class f of nonempty subsets of e a weight w e r and a cost c e r for each e e c e stands for the cost of reducing weight w e by one unit for each subset f f the bottleneck weight of f is w f min e f w e the weight of the family f is the maximum of w f for all f in f the problem is to determine new weights x e w e such that the weight of f is minimized under the constraint that the overall reduction cost does not exceed a given budget b similarly to capacity expansion problems wrps include np hard problems a wrp can be formulated as a parametric optimization problem over all transversal sets t of the class f this leads to strongly polynomial solution procedures for special systems f in particular we outline a polynomial algorithm in the case when f is the class of all spanning trees in an undirected graph

solving inverse spanning tree problems through network flow techniques given a solution x and an a priori estimated cost vector c the inverse optimization problem is to identify another cost vector d so that x is optimal with respect to the cost vector d and its deviation from c is minimum in this paper we consider the inverse spanning tree problem on an undirected graph g n a with n nodes and m arcs and where the deviation between c and d is defined by the rectilinear distance between the two vectors that is l1 norm we show that the inverse spanning tree problem can be formulated as the dual of an assignment problem on a bipartite network g0 n0 a0 with math not displayed and math not displayed the bipartite ne twork satisfies the property that n1 n 1 n2 m n 1 and a0 o nm in general n1 n2 using this special structure of the assignment problem we develop a specific implementation of the successive shortest path algorithm that runs in o n3 time we also consider the weighted version of the inverse spanning tree problem in which the objective function is to minimize the sum of the weighted deviations of arcs the weighted inverse spanning tree can be formulated as the dual of the transportation problem using a cost scaling algorithm this transportation problem can be solved in o n2m log nc time where c denotes the largest arc cost in the data finally we consider a minimax version of the inverse spanning tree problem and show that it can be solved in o n2 time

i o efficient algorithms for the minimum cut problem on unweighted undirected graphs the problem of finding the minimum cut of an undirected unweighted graph is studied on the external memory model first a lower bound of e v sort v on the number of i os is shown for the problem where v is the number of vertices and e is the number of edges then the following are presented for m b 2 1 a minimum cut algorithm that uses o c log e rm msf v e frac v b rm sort v i os here msf v e is the number of i os needed to compute a minimum spanning tree of the graph and c is the value of the minimum cut the algorithm performs better on dense graphs than the algorithm of 7 which requires o e c 2 v log v c i os when executed on the external memory model for a fat graph for 0 the maximum tree packing of the graph is at least 1 c 2 our algorithm computes a minimum cut in o c loge msf v e sort e i os 2 a randomized algorithm that computes minimum cut with high probability in o c log e cdot rm msf v e rm sort e log 2 v frac v b rm sort v log v i os 3 a 2 e minimum cut algorithm that requires o e v msf v e i os and performs better on sparse graphs than our exact minimum cut algorithm

up and downgrading the 1 center in a network abstract we study budget constrained network improvement and degrading problems based on the vertex 1 center problem on graphs given a graph with vertex weights and edge lengths the task is to decrease and increase the vertex weights within certain limits such that the optimal 1 center objective value with respect to the new weights is minimized and maximized respectively the upgrading improvement problem is shown to be solvable in o n 2 time provided that the distance matrix is given the downgrading 1 center problem is shown to be strongly np hard on general graphs but can be solved in o n 2 time on trees as byproduct we suggest an algorithm that solves the problem of minimizing over the upper envelope of n piecewise linear functions in o k n time where k is the total number of breakpoints

some reverse location problems abstract the general location problem in a network is to find locations of facilities in a given network such that the total cost is minimum it is very often to have its reverse case in which the facilities have already been located on the network and the problem is how to improve the network within a given budget so that the improved network is as efficient as possible in this paper we present a strongly polynomial algorithm for a reverse location problem in tree networks the method can be extended to solve reverse two or more location problems

existence and partial regularity results for the heat flow for harmonic maps on considere le probleme d evolution t u m u n u 0 dans m r u 0 u 0 sur m ou m et n sont des varietes de riemann lisses compactes et u 0 l application harmonique de m dans n on demontre l existence d une solution globale faible

inverse chromatic number problems in interval and permutation graphs abstract given a graph g and a positive integer k the inverse chromatic number problem consists in modifying the graph as little as possible so that it admits a chromatic number not greater than k in this paper we focus on the inverse chromatic number problem for certain classes of graphs first we discuss diverse possible versions and then focus on two application frameworks which motivate this problem in interval and permutation graphs the inverse booking problem and the inverse track assignment problem the inverse booking problem is closely related to some previously known scheduling problems we propose new hardness results and polynomial cases the inverse track assignment problem motivates our study of the inverse chromatic number problem in permutation graphs we show how to solve in polynomial time a generalization of the problem with a bounded number of colors

on the use of an inverse shortest paths algorithm for recovering linearly correlated costs this paper considers the inverse shortest paths problem where arc costs are subject to correlation constraints the motivation for this research arises from applications in traffic modelling and seismic tomography a new method is proposed for solving this class of problems it is constructed as a generalization of the algorithm presented in burton and toint mathematical programming 53 1992 for uncorrelated inverse shortest paths preliminary numerical experience with the new method is presented and discussed

inverse optimization for linearly constrained convex separable programming problems abstract in this paper we study inverse optimization for linearly constrained convex separable programming problems that have wide applications in industrial and managerial areas for a given feasible point of a convex separable program the inverse optimization is to determine whether the feasible point can be made optimal by adjusting the parameter values in the problem and when the answer is positive find the parameter values that have the smallest adjustments a sufficient and necessary condition is given for a feasible point to be able to become optimal by adjusting parameter values inverse optimization formulations are presented with l 1 and l 2 norms these inverse optimization problems are either linear programming when l 1 norm is used in the formulation or convex quadratic separable programming when l 2 norm is used

computational aspects of the inverse single facility location problem on trees under lk norm abstract we consider in this paper the inverse versions of the two popular problems in location theory say the 1 median and the 1 center problems on trees the cost for modifying vertex weights is measured under l k norm for a positive integer k and hence the cost function is nonlinear for the inverse 1 median problem we develop a linear time algorithm based on the optimal solution of the induced unconstrained problem for the inverse 1 center problem we prove that the problem can be decomposed into linearly many subproblems and the objective function in each subproblem is piecewise convex furthermore we also discuss an o n log n time algorithm for the inverse 1 center problem under l 2 norm based on the convexity of the cost function of each subproblem

hausdorff measure of the singular set of landau lifshitz equations with a nonlocal term this paper is concerned with the partial regularity of the stationary solutions to the landau lifshitz system of ferromagnetic spin chain with gilbert damping and a nonlocal term in 3 dimensions the hausdorff measure of the singular set is discussed

a class of node based bottleneck improvement problems abstract in this paper we consider a class of node based bottleneck improvement problems with respect to the system v e f where v is a node set e is an edge set and f 2 e is a nonempty family of subsets of e in the node based upgrading model a node v can be upgraded at the expense of c v and such an upgrade reduces weights on all edges incident to v for a given budget b the objective is to upgrade a subset of nodes s v such that the bottleneck weight of the family f is minimum under the constraint that the overall upgrade cost c s does not exceed b the problem includes some np hard cases for the special tree path system v e f in which t v e is a rooted tree and f is a set of paths from the root to the leaves we present an o n log n algorithm where n v we also consider some variations of this problem some related complexity results and algorithms are also presented

partial regularity for stationary harmonic maps into spheres in an interesting recent paper 12 f hi lein has shown that any weakly harmonic mapping from a two dimensional surface into a sphere is smooth i present here a kind of generalization to higher dimensions asserting in effect that a stationary harmonic mapping from an open subset of nn n 3 into a sphere is smooth except possibly for a closed singular set of n 2 dimensional hausdorff measure zero my proof crucially depends upon several of h l in s observations as streamlined by p l lions to state the result precisely let us suppose that m n 2 u is a smooth open subset of nn and s m 1 denotes the unit sphere in nm a function u in the sobolev space hi u rm u u 1 urn belongs to h i u s ml provided t u 1 a e in u

partial regularity for weak heat flows into spheres in this paper we show that a weak heat flow of harmonic maps from a compact riemannian manifold possibly with boundary into a sphere satisfying the monotonicity inequality and the energy inequality is regular off a closed set of m dimensional hausdorff measure zero

inverse polynomial optimization we consider the inverse optimization problem associated with the polynomial program f min f bx colon bx in k and a given current feasible solution y in k we provide a systematic numerical scheme to compute an inverse optimal solution that is we compute a polynomial tilde f which may be of the same degree as f if desired with the following properties a y is a global minimizer of tilde f on k with a putinar s certificate with an a priori degree bound d fixed and b tilde f minimizes vert f tilde f vert which can be the l1 l2 or l norm of the coefficients over all polynomials with such properties computing tilde f d reduces to solving a semidefinite program whose optimal value also provides a bound on how far fy is from the unknown optimal value f the size of the semidefinite program can be adapted to the available computational capabilities moreover if one uses the l1 norm then tilde f takes a simple and explicit canonical form some variations are also discussed

algorithm for constraint partial inverse matroid problem with weight increase forbidden in a partial inverse matroid problem given a matroid m s i a real valued weight function w on s and an independent set i 0 i the goal is to modify the weight w as small as possible to a new weight w such that there exists a w maximum base containing i 0 in this paper we study a constraint version of the partial inverse matroid problem in which the weight can only be decreased a polynomial time algorithm is presented under l norm

an inverse dea model for inputs outputs estimate abstract in this paper we discuss such problems if among a group of decision making units we increase certain inputs to a particular unit and assume that the dmu maintains its current efficiency level with respect to other units how much more outputs could the unit produce or if the outputs need to be increased to a certain level and the efficiency of the unit remains unchanged how much more inputs should be provided to the unit we treat them as inverse data envelopment analysis dea problems and propose a method to solve such problems the problem is transformed into a multi objective programming problem to solve though in some special cases it can be answered by solving just one single object lp problem we use two examples to illustrate our computation method

constrained clustering by constraint programming cluster analysis is an important task in data mining with hundreds of different approaches in the literature since the last decade the cluster analysis has been extended to constrained clustering also called semi supervised clustering so as to integrate previous knowledge on data to clustering algorithms in this dissertation we explore constraint programming cp for solving the task of constrained clustering the main principles in cp are 1 users specify declaratively the problem in a constraint satisfaction problem 2 solvers search for solutions by constraint propagation and search relying on cp has two main advantages the declarativity which enables to easily add new constraints and the ability to find an optimal solution satisfying all the constraints when there exists one we propose two models based on cp to address constrained clustering tasks the models are flexible and general and supports instance level constraints and different cluster level constraints it also allows the users to choose among different optimization criteria in order to improve the efficiency different aspects have been studied in the dissertation experiments on various classical datasets show that our models are competitive with other exact approaches we show that our models can easily be embedded in a more general process and we illustrate this on the problem of finding the pareto front of a bi criterion optimization process

some inverse optimization problems under the hamming distance given a feasible solution to a particular combinatorial optimization problem defined on a graph and a cost vector defined on the arcs of the graph the corresponding inverse problem is to disturb the cost vector such that the feasible solution becomes optimal the aim is to optimize the difference between the initial cost vector and the disturbed one this difference can be measured in several ways we consider the hamming distance measuring in how many components two vectors are different where weights are associated to the components general algorithms for the bottleneck or minimax criterion are described and after modification applied to the inverse minimum spanning tree problem the inverse shortest path tree problem and the linear assignment problem

diffuse interface models on graphs for classification of high dimensional data this paper is a republication of an mms paper a l bertozzi and a flenner multiscale model simul 10 2012 pp 1090 1118 describing a new class of algorithms for classification of high dimensional data these methods combine ideas from spectral methods on graphs with nonlinear edge region detection methods traditionally used in the pde based imaging community the algorithms use the ginzburg landau functional extended to a graphical framework which has classical pde connections to total variation minimization convex splitting algorithms allow us to quickly find minimizers of the proposed model and take advantage of fast spectral solvers of linear graph theoretic problems we review the diverse computational examples presented in the original paper involving both basic clustering and semisupervised learning for different applications case studies include feature identification in images segmentation in social networks and segmentation of shapes in high dimensional datasets since the pape

the inverse fermat weber problem abstract given n points in the plane with nonnegative weights the inverse fermat weber problem consists in changing the weights at minimum cost such that a prespecified point in the plane becomes the euclidean 1 median the cost is proportional to the increase or decrease of the corresponding weight in case that the prespecified point does not coincide with one of the given n points the inverse fermat weber problem can be formulated as linear program we derive a purely combinatorial algorithm which solves the inverse fermat weber problem with unit cost using o n greedy like iterations where each of them can be done in constant time if the points are sorted according to their slopes if the prespecified point coincides with one of the given n points it is shown that the corresponding inverse problem can be written as convex problem and hence is solvable in polynomial time to any fixed precision

the inverse optimal value problem this paper considers the following inverse optimization problem given a linear program a desired optimal objective value and a set of feasible cost vectors determine a cost vector such that the corresponding optimal objective value of the linear program is closest to the desired value the above problem referred here as the inverse optimal value problem is significantly different from standard inverse optimization problems that involve determining a cost vector for a linear program such that a pre specified solution vector is optimal in this paper we show that the inverse optimal value problem is np hard in general we identify conditions under which the problem reduces to a concave maximization or a concave minimization problem we provide sufficient conditions under which the associated concave minimization problem and correspondingly the inverse optimal value problem is polynomially solvable for the case when the set of feasible cost vectors is polyhedral we describe an algorithm for the inverse optimal value problem based on solving linear and bilinear programming problems some preliminary computational experience is reported

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

data driven inverse optimization with imperfect information in data driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal thus the observer seeks the agent s objective function that best explains a historical sequence of signals and corresponding optimal actions we formalize this inverse optimization problem as a distributionally robust program minimizing the worst case risk that the estimated decision i e the decision implied by a particular candidate objective differs from the agent s actual response to a random signal we show that our framework offers attractive out of sample performance guarantees for different prediction errors and that the emerging inverse optimization problems can be reformulated as or approximated by tractable convex programs when the prediction error is measured in the space of objective values a main strength of the proposed approach is that it naturally generalizes to situations where the observer has imperfect information e g when the agent s true objective function is not contained in the space of candidate objectives when the agent suffers from bounded rationality or implementation errors or when the observed signal response pairs are corrupted by measurement noise

sparse spectral clustering method based on the incomplete cholesky decomposition a novel sparse spectral clustering method using linear algebra techniques is proposed spectral clustering methods solve an eigenvalue problem containing a graph laplacian the proposed method exploits the structure of the laplacian to construct an approximation not in terms of a low rank approximation but in terms of capturing the structure of the matrix with this approximation the size of the eigenvalue problem can be reduced to obtain the indicator vectors from the eigenvectors the method proposed by zha et al 2002 26 which computes a pivoted lq factorization of the eigenvector matrix is adapted this formulation also gives the possibility to extend the method to out of sample points

a numerically stable dual method for solving strictly convex quadratic programs an efficient and numerically stable dual algorithm for positive definite quadratic programming is described which takes advantage of the fact that the unconstrained minimum of the objective function can be used as a starting point its implementation utilizes the cholesky and qr factorizations and procedures for updating them the performance of the dual algorithm is compared against that of primal algorithms when used to solve randomly generated test problems and quadratic programs generated in the course of solving nonlinear programming problems by a successive quadratic programming code the principal motivation for the development of the algorithm these computational results indicate that the dual algorithm is superior to primal algorithms when a primal feasible point is not readily available the algorithm is also compared theoretically to the modified simplex type dual methods of lemke and van de panne and whinston and it is illustrated by a numerical example

generalized inverse multiobjective optimization with application to cancer therapy we generalize the standard method of solving inverse optimization problems to allow for the solution of inverse problems that would otherwise be ill posed or infeasible in multiobjective linear optimization given a solution that is not a weakly efficient solution to the forward problem our method generates objective function weights that make the given solution a near weakly efficient solution our generalized inverse optimization model specializes to the standard model when the given solution is weakly efficient and retains the complexity of the underlying forward problem we provide a novel interpretation of our inverse formulation as the dual of the well known benson s method and by doing so develop a new connection between inverse optimization and pareto surface approximation techniques we apply our method to prostate cancer data obtained from princess margaret cancer centre in toronto canada we demonstrate that clinically acceptable treatments can be generated using a small number of objective

deterministic edge connectivity in near linear time we present a deterministic algorithm that computes the edge connectivity of a graph in near linear time this is for a simple undirected unweighted graph g with n vertices and m edges this is the first o mn time deterministic algorithm for the problem our algorithm is easily extended to find a concrete minimum edge cut in fact we can construct the classic cactus representation of all minimum cuts in near linear time the previous fastest deterministic algorithm by gabow from stoc 91 took o m 2 n where is the edge connectivity but can be as big as n 1 karger presented a randomized near linear time monte carlo algorithm for the minimum cut problem at stoc 96 but the returned cut is only minimum with high probability our main technical contribution is a near linear time algorithm that contracts vertex sets of a simple input graph g with minimum degree producing a multigraph with o m edges which preserves all minimum cuts of g with at least two vertices on each side in our deterministic near linear time algorithm we will decompose the problem via low conductance cuts found using pagerank a la brin and page 1998 as analyzed by andersson chung and lang at focs 06 normally such algorithms for low conductance cuts are randomized monte carlo algorithms because they rely on guessing a good start vertex however in our case we have so much structure that no guessing is needed

the brunn minkowski inequality in 1978 osserman 124 wrote an extensive survey on the isoperimetric inequality the brunn minkowski inequality can be proved in a page yet quickly yields the classical isoperimetric inequality for important classes of subsets of rn and deserves to be better known this guide explains the relationship between the brunn minkowski inequality and other inequalities in geometry and analysis and some applications

optimal algorithms for inverse vertex obnoxious center location problems on graphs abstract in an inverse vertex obnoxious center location problem the aim is to modify the edge lengths at minimum total cost with respect to the modification bounds such that a predetermined vertex becomes a vertex obnoxious center location under the new edge lengths we develop a linear time combinatorial method for the problem with edge length augmentation for the reduction case an algorithm with cubic running time is devised we also show that the problem with both edge length augmentation and reduction can be solved in sextic time

a further study on inverse linear programming problems abstract in this paper we continue our previous study zhang and liu j comput appl math 72 1996 261 273 on inverse linear programming problems which requires us to adjust the cost coefficients of a given lp problem as less as possible so that a known feasible solution becomes the optimal one in particular we consider the cases in which the given feasible solution and one optimal solution of the lp problem are 0 1 vectors which often occur in network programming and combinatorial optimization and give very simple methods for solving this type of inverse lp problems besides instead of the commonly used l1 measure we also consider the inverse lp problems under l measure and propose solution methods

a dual active set algorithm for positive semi definite quadratic programming because of the many important applications of quadratic programming fast and efficient methods for solving quadratic programming problems are valued goldfarb and idnani 1983 describe one such method well known to be efficient and numerically stable the goldfarb and idnani method suffers only from the restriction that in its original form it cannot be applied to problems which are positive semi definite rather than positive definite in this paper we present a generalization of the goldfarb and idnani method to the positive semi definite case and prove finite termination of the generalized algorithm in our generalization we preserve the spirit of the goldfarb and idnani method and extend their numerically stable implementation in a natural way

inverse 1 median problem on trees under mixed rectilinear and chebyshev norms abstract we consider in this paper the inverse 1 median problem on trees with variable vertex weights which are partitioned into groups while the modifications in each group are measured by chebyshev norm rectilinear norm is applied for computing the cost of groups and vice versa as a result it yields the sum of max and the max of sum objective functions for the sum of max objective we develop an o m log m time algorithm based on a parameterization approach where m is the number of vertices in the tree on the other hand the problem under the max of sum objective can be solved in linear time by an algorithm that prunes a half of indices in each iteration

a simple min cut algorithm we present an algorithm for finding the minimum cut of an undirected edge weighted graph it is simple in every respect it has a short and compact description is easy to implement and has a surprisingly simple proof of correctness its runtime matches that of the fastest algorithm known the runtime analysis is straightforward in contrast to nearly all approaches so far the algorithm uses no flow techniques roughly speaking the algorithm consists of about v nearly identical phases each of which is a maximum adjacency search

a new approach to the maximum flow problem all previously known efficient maximum flow algorithms work by finding augmenting paths either one path at a time as in the original ford and fulkerson algorithm or all shortest length augmenting paths at once using the layered network approach of dinic an alternative method based on the preflow concept of karzanov is introduced a preflow is like a flow except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out the method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths the algorithm and its analysis are simple and intuitive yet the algorithm runs as fast as any other known method on dense graphs achieving an o n 3 time bound on an n vertex graph by incorporating the dynamic tree data structure of sleator and tarjan we obtain a version of the algorithm running in o nm log n 2 m time on an n vertex m edge graph this is as fast as any known method for any graph density and faster on graphs of moderate density the algorithm also admits efficient distributed and parallel implementations a parallel implementation running in o n 2 log n time using n processors and o m space is obtained this time bound matches that of the shiloach vishkin algorithm which also uses n processors but requires o n 2 space

existence of partially regular weak solutions to landau lifshitz maxwell equations abstract in this paper the authors establish the existence of partially regular weak solutions to the landau lifshitz equations coupling with static maxwell systems in 3 dimensions by ginzburg landau approximation it is proved that the hausdorff measure of the singular set is locally finite this extends the similar results of ding and guo s ding b guo hausdorff measure of the singular set of landau lifshitz equations with a nonlocal term comm math phys 250 1 2004 95 117 from the stationary solutions to weak solutions and the results of wang c wang on landau lifshitz equations in dimensions at most four indiana univ math j 55 5 2006 1615 1644 from landau lifshitz equations to landau lifshitz maxwell equations

on the inverse problem of linear programming and its application to minimum weight perfect k matching we first introduce the inverse problem of linear programming we then apply it to the inverse problem of minimum weight perfect k matching of bipartite graphs we show that there is a strongly polynomial algorithm for solving the problem

consensus and products of random stochastic matrices exact rate for convergence in probability we find the exact rate for convergence in probability of products of independent identically distributed symmetric stochastic matrices it is well known that if the matrices have positive diagonals almost surely and the support graph of the mean or expected value of the random matrices is connected the products of the matrices converge almost surely to the average consensus matrix and thus in probability in this paper we show that the convergence in probability is exponentially fast and we explicitly characterize the exponential rate of this convergence our analysis reveals that the exponential rate of convergence in probability depends only on the statistics of the support graphs of the random matrices further we show how to compute this rate for commonly used random models gossip and link failure with these models the rate is found by solving a min cut problem and hence it is easily computable finally as an illustration we apply our results to solving power allocation among networked sensors in a consensus innovations distributed detection problem