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

complex multiplication cycles and kudla rapoport divisors we study the intersections of special cycles on a unitary shimura variety of signature n 1 1 and show that the intersection multiplicities of these cycles agree with fourier coefficients of eisenstein series the results are new cases of conjectures of kudla and suggest a gross zagier theorem for unitary shimura varieties

borcherds products and arithmetic intersection theory on hilbert modular surfaces we prove an arithmetic version of a theorem of hirzebruch and zagier saying that hirzebruch zagier divisors on a hilbert modular surface are the coecients of an elliptic modular form of weight two moreover we determine the arithmetic selfintersection number of the line bundle of modular forms equipped with its petersson metric on a regular model of a hilbert modular surface and study faltings heights of arithmetic hirzebruch zagier divisors

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

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

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

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

special cycles on unitary shimura varieties i unramified local theory the supersingular locus in the fiber at p of a shimura variety attached to a unitary similitude group gu 1 n 1 over is uniformized by a formal scheme mathcal n in the case when p is an inert prime we define special cycles mathcal z bold x in mathcal n associated to collections bold x of m special homomorphisms with fundamental matrix t hermm ok when m n and t is nonsingular we show that the cycle mathcal z bold x is either empty or is a union of components of the ekedahl oort stratification and we give a necessary and sufficient condition in terms of t for mathcal z bold x to be irreducible when mathcal z bold x is zero dimensional in which case it reduces to a single point we determine the length of the corresponding local ring by using a variant of the theory of quasi canonical liftings we show that this length coincides with the derivative of a representation density for hermitian forms

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

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

the partial inverse minimum spanning tree problem when weight increase is forbidden abstract in a partial inverse optimization problem there is an underlying optimization problem with a partially given solution the objective is to find a minimal perturbation of some of the problem s parameter values in such a way that the partial solution becomes a part of the optimal solution we consider the partial inverse minimum spanning tree problem in an undirected weighted graph under the constraint that edge weights can not be increased by decreasing one or more edge weights as little as possible a given forest must be presented in the new minimum spanning tree under a quite general criterion function evaluating the proposed decreases of weight we show that this problem can be solved in polynomial time

heights of kudla rapoport divisors and derivatives of l functions we study special cycles on integral models of shimura varieties associated with unitary similitude groups of signature n 1 1 we construct an arithmetic theta lift from harmonic maass forms of weight 2 n to the arithmetic chow group of the integral model of a unitary shimura variety by associating to a harmonic maass form f a linear combination of kudla rapoport divisors equipped with the green function given by the regularized theta lift of f our main result is an equality of two complex numbers 1 the height pairing of the arithmetic theta lift of f against a cm cycle and 2 the central derivative of the convolution l function of a weight n cusp form depending on f and the theta function of a positive definite hermitian lattice of rank n 1 when specialized to the case n 2 this result can be viewed as a variant of the gross zagier formula for shimura curves associated to unitary groups of signature 1 1 the proof relies on among other things a new method for computing improper arithmetic intersections

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

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

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

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

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

faltings heights of abelian varieties with complex multiplication let m be the shimura variety associated with the group of spinor similitudes of a quadratic space over q of signature n 2 we prove a conjecture of bruinier kudla yang relating the arithmetic intersection multiplicities of special divisors and big cm points on m to the central derivatives of certain l functions as an application of this result we prove an averaged version of colmez s conjecture on the faltings heights of cm abelian varieties

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

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

periodic simple groups of finitary linear transformations a group is locally finite if every finite subset generates a finite subgroup a group of linear transformations is finitary if each element minus the identity is an endomorphism of finite rank the classification and structure theory for locally finite simple groups splits naturally into two cases those groups that can be faithfully represented as groups of finitary linear transformations and those groups that are not finitary linear this paper completes the finitary case we classify up to isomorphism those infinite locally finite simple groups that are finitary linear but not linear

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

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

complex multiplication cycles and kudla rapoport divisors ii we study the intersections of special cycles on a unitary shimura variety of signature n 1 1 and show that the intersection multiplicities of these cycles agree with fourier coecients of eisenstein series the results are new cases of conjectures of kudla and suggest a gross zagier theorem for unitary shimura varieties

on generalized finitary groups we introduce a wide range of generalized finitary automorphism groups of an arbitrary module m over an arbitrary ring r the largest such subgroup of autrm that we seriously consider here is the subgroup of all r automorphisms g of m such that m g 1 has krull dimension we also consider the subgroup of all r automorphisms g of m such that m g 1 is artinian as an r module the results are vaguely analogous to the genuine finitary case but are somewhat weaker