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  • Lipschitz-like property relative to a set and the generalized Mordukhovich criterion
    Math. Program. (IF 2.823) Pub Date : 2020-09-25
    K. W. Meng, M. H. Li, W. F. Yao, X. Q. Yang

    In this paper we will establish some necessary condition and sufficient condition respectively for a set-valued mapping to have the Lipschitz-like property relative to a closed set by employing regular normal cone and limiting normal cone of a restricted graph of the set-valued mapping. We will obtain a complete characterization for a set-valued mapping to have the Lipschitz-property relative to a

    更新日期:2020-09-25
  • Complete positivity and distance-avoiding sets
    Math. Program. (IF 2.823) Pub Date : 2020-09-16
    Evan DeCorte, Fernando Mário de Oliveira Filho, Frank Vallentin

    We introduce the cone of completely positive functions, a subset of the cone of positive-type functions, and use it to fully characterize maximum-density distance-avoiding sets as the optimal solutions of a convex optimization problem. As a consequence of this characterization, it is possible to reprove and improve many results concerning distance-avoiding sets on the sphere and in Euclidean space

    更新日期:2020-09-16
  • Convex graph invariant relaxations for graph edit distance
    Math. Program. (IF 2.823) Pub Date : 2020-09-16
    Utkan Onur Candogan, Venkat Chandrasekaran

    The edit distance between two graphs is a widely used measure of similarity that evaluates the smallest number of vertex and edge deletions/insertions required to transform one graph to another. It is NP-hard to compute in general, and a large number of heuristics have been proposed for approximating this quantity. With few exceptions, these methods generally provide upper bounds on the edit distance

    更新日期:2020-09-16
  • New limits of treewidth-based tractability in optimization
    Math. Program. (IF 2.823) Pub Date : 2020-09-15
    Yuri Faenza, Gonzalo Muñoz, Sebastian Pokutta

    Sparse structures are frequently sought when pursuing tractability in optimization problems. They are exploited from both theoretical and computational perspectives to handle complex problems that become manageable when sparsity is present. An example of this type of structure is given by treewidth: a graph theoretical parameter that measures how “tree-like” a graph is. This parameter has been used

    更新日期:2020-09-15
  • Accelerating variance-reduced stochastic gradient methods
    Math. Program. (IF 2.823) Pub Date : 2020-09-15
    Derek Driggs, Matthias J. Ehrhardt, Carola-Bibiane Schönlieb

    Variance reduction is a crucial tool for improving the slow convergence of stochastic gradient descent. Only a few variance-reduced methods, however, have yet been shown to directly benefit from Nesterov’s acceleration techniques to match the convergence rates of accelerated gradient methods. Such approaches rely on “negative momentum”, a technique for further variance reduction that is generally specific

    更新日期:2020-09-15
  • Complexity of stochastic dual dynamic programming
    Math. Program. (IF 2.823) Pub Date : 2020-09-15
    Guanghui Lan

    Stochastic dual dynamic programming is a cutting plane type algorithm for multi-stage stochastic optimization originated about 30 years ago. In spite of its popularity in practice, there does not exist any analysis on the convergence rates of this method. In this paper, we first establish the number of iterations, i.e., iteration complexity, required by a basic dual dynamic programming method for solving

    更新日期:2020-09-15
  • Closed convex sets with an open or closed Gauss range
    Math. Program. (IF 2.823) Pub Date : 2020-09-08
    Juan Enrique Martínez-Legaz, Cornel Pintea

    We characterize the closed convex subsets of \({\mathbb {R}}^{n}\) which have open or closed Gauss ranges. Some special attention is paid to epigraphs of lower semicontinuous convex functions.

    更新日期:2020-09-08
  • A loose Benders decomposition algorithm for approximating two-stage mixed-integer recourse models
    Math. Program. (IF 2.823) Pub Date : 2020-09-07
    Niels van der Laan, Ward Romeijnders

    We propose a new class of convex approximations for two-stage mixed-integer recourse models, the so-called generalized alpha-approximations. The advantage of these convex approximations over existing ones is that they are more suitable for efficient computations. Indeed, we construct a loose Benders decomposition algorithm that solves large problem instances in reasonable time. To guarantee the performance

    更新日期:2020-09-08
  • Fully asynchronous stochastic coordinate descent: a tight lower bound on the parallelism achieving linear speedup
    Math. Program. (IF 2.823) Pub Date : 2020-09-07
    Yun Kuen Cheung, Richard Cole, Yixin Tao

    We seek tight bounds on the viable parallelism in asynchronous implementations of coordinate descent that achieves linear speedup. We focus on asynchronous coordinate descent (ACD) algorithms on convex functions which consist of the sum of a smooth convex part and a possibly non-smooth separable convex part. We quantify the shortfall in progress compared to the standard sequential stochastic gradient

    更新日期:2020-09-08
  • Strongly stable C-stationary points for mathematical programs with complementarity constraints
    Math. Program. (IF 2.823) Pub Date : 2020-08-19
    Daniel Hernández Escobar, Jan-J. Rückmann

    In this paper we consider the class of mathematical programs with complementarity constraints (MPCC). Under an appropriate constraint qualification of Mangasarian–Fromovitz type we present a topological and an equivalent algebraic characterization of a strongly stable C-stationary point for MPCC. Strong stability refers to the local uniqueness, existence and continuous dependence of a solution for

    更新日期:2020-08-19
  • Asymptotic behavior of solutions: An application to stochastic NLP
    Math. Program. (IF 2.823) Pub Date : 2020-08-18
    Arnab Sur, John R. Birge

    In this article we study the consistency of optimal and stationary (KKT) points of a stochastic non-linear optimization problem involving expectation functionals, when the underlying probability distribution associated with the random variable is weakly approximated by a sequence of random probability measures. The optimization model includes constraints with expectation functionals those are not captured

    更新日期:2020-08-18
  • A smooth homotopy method for incomplete markets
    Math. Program. (IF 2.823) Pub Date : 2020-08-12
    Yang Zhan, Chuangyin Dang

    In the general equilibrium with incomplete asset markets (GEI) model, the excess demand functions are typically not continuous at the prices for which the assets have redundant returns. The reason is that, at these prices, the return matrix drops rank and households’ budget sets collapse suddenly. This discontinuity results in a serious problem for the existence and computation of general equilibrium

    更新日期:2020-08-12
  • Computation and efficiency of potential function minimizers of combinatorial congestion games
    Math. Program. (IF 2.823) Pub Date : 2020-08-11
    Pieter Kleer, Guido Schäfer

    We study the computation and efficiency of pure Nash equilibria in combinatorial congestion games, where the strategies of each player i are given by the binary vectors of a polytope \(P_i\). Our main goal is to understand which structural properties of such polytopal congestion games enable us to derive an efficient equilibrium selection procedure to compute pure Nash equilibria with attractive social

    更新日期:2020-08-11
  • Connecting optimization with spectral analysis of tri-diagonal matrices
    Math. Program. (IF 2.823) Pub Date : 2020-08-08
    Jean B. Lasserre

    We show that the global minimum (resp. maximum) of a continuous function on a compact set can be approximated from above (resp. from below) by computing the smallest (rest. largest) eigenvalue of a hierarchy of \((r\times r)\) tri-diagonal matrices of increasing size. Equivalently it reduces to computing the smallest (resp. largest) root of a certain univariate degree-r orthonormal polynomial. This

    更新日期:2020-08-09
  • Determination of convex functions via subgradients of minimal norm
    Math. Program. (IF 2.823) Pub Date : 2020-08-06
    Pedro Pérez-Aros, David Salas, Emilio Vilches

    We show, in Hilbert space setting, that any two convex proper lower semicontinuous functions bounded from below, for which the norm of their minimal subgradients coincide, they coincide up to a constant. Moreover, under classic boundary conditions, we provide the same results when the functions are continuous and defined over an open convex domain. These results show that for convex functions bounded

    更新日期:2020-08-06
  • Prophet secretary through blind strategies
    Math. Program. (IF 2.823) Pub Date : 2020-08-03
    Jose Correa, Raimundo Saona, Bruno Ziliotto

    In the classic prophet inequality, a well-known problem in optimal stopping theory, samples from independent random variables (possibly differently distributed) arrive online. A gambler who knows the distributions, but cannot see the future, must decide at each point in time whether to stop and pick the current sample or to continue and lose that sample forever. The goal of the gambler is to maximize

    更新日期:2020-08-03
  • The confined primal integral: a measure to benchmark heuristic MINLP solvers against global MINLP solvers
    Math. Program. (IF 2.823) Pub Date : 2020-07-29
    Timo Berthold, Zsolt Csizmadia

    It is a challenging task to fairly compare local solvers and heuristics against each other and against global solvers. How does one weigh a faster termination time against a better quality of the found solution? In this paper, we introduce the confined primal integral, a new performance measure that rewards a balance of speed and solution quality. It emphasizes the early part of the solution process

    更新日期:2020-07-29
  • Lipschitz modulus of linear and convex inequality systems with the Hausdorff metric
    Math. Program. (IF 2.823) Pub Date : 2020-07-28
    G. Beer, M. J. Cánovas, M. A. López, J. Parra

    This paper analyzes the Lipschitz behavior of the feasible set mapping associated with linear and convex inequality systems in \({\mathbb {R}}^{n}\). To start with, we deal with the parameter space of linear (finite/semi-infinite) systems identified with the corresponding sets of coefficient vectors, which are assumed to be closed subsets of \({\mathbb {R}} ^{n+1}\). In this framework the size of perturbations

    更新日期:2020-07-28
  • New extremal principles with applications to stochastic and semi-infinite programming
    Math. Program. (IF 2.823) Pub Date : 2020-07-23
    Boris S. Mordukhovich, Pedro Pérez-Aros

    This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These extremal principles concern measurable set-valued mappings/multifunctions with values in finite-dimensional spaces and are established in both approximate and exact

    更新日期:2020-07-23
  • Characterization of Filippov representable maps and Clarke subdifferentials
    Math. Program. (IF 2.823) Pub Date : 2020-07-16
    Mira Bivas, Aris Daniilidis, Marc Quincampoix

    The ordinary differential equation \(\dot{x}(t)=f(x(t)), \; t \ge 0 \), for f measurable, is not sufficiently regular to guarantee existence of solutions. To remedy this we may relax the problem by replacing the function f with its Filippov regularization \(F_{f}\) and consider the differential inclusion \(\dot{x}(t)\in F_{f}(x(t))\) which always has a solution. It is interesting to know, inversely

    更新日期:2020-07-16
  • Strengthening convex relaxations of 0/1-sets using Boolean formulas
    Math. Program. (IF 2.823) Pub Date : 2020-07-15
    Samuel Fiorini, Tony Huynh, Stefan Weltge

    In convex integer programming, various procedures have been developed to strengthen convex relaxations of sets of integer points. On the one hand, there exist several general-purpose methods that strengthen relaxations without specific knowledge of the set S of feasible integer points, such as popular linear programming or semi-definite programming hierarchies. On the other hand, various methods have

    更新日期:2020-07-15
  • Quasi-Monte Carlo methods for two-stage stochastic mixed-integer programs
    Math. Program. (IF 2.823) Pub Date : 2020-07-14
    H. Leövey, W. Römisch

    We consider randomized QMC methods for approximating the expected recourse in two-stage stochastic optimization problems containing mixed-integer decisions in the second stage. It is known that the second-stage optimal value function is piecewise linear-quadratic with possible kinks and discontinuities at the boundaries of certain convex polyhedral sets. This structure is exploited to provide conditions

    更新日期:2020-07-14
  • A new framework to relax composite functions in nonlinear programs
    Math. Program. (IF 2.823) Pub Date : 2020-07-13
    Taotao He, Mohit Tawarmalani

    In this paper, we devise new relaxations for composite functions, which improve the prevalent factorable relaxations, without introducing additional variables, by exploiting the inner-function structure. We outer-approximate inner-functions using arbitrary under- and over-estimators and then convexify the outer-function over a polytope P, which models the ordering relationships between the inner-functions

    更新日期:2020-07-13
  • Generalized Chvátal-Gomory closures for integer programs with bounds on variables
    Math. Program. (IF 2.823) Pub Date : 2020-07-10
    Sanjeeb Dash, Oktay Günlük, Dabeen Lee

    Integer programming problems that arise in practice often involve decision variables with one or two sided bounds. In this paper, we consider a generalization of Chvátal-Gomory inequalities obtained by strengthening Chvátal-Gomory inequalities using the bounds on the variables. We prove that the closure of a rational polyhedron obtained after applying the generalized Chvátal-Gomory inequalities is

    更新日期:2020-07-10
  • The sum-of-squares hierarchy on the sphere and applications in quantum information theory
    Math. Program. (IF 2.823) Pub Date : 2020-07-06
    Kun Fang, Hamza Fawzi

    We consider the problem of maximizing a homogeneous polynomial on the unit sphere and its hierarchy of sum-of-squares relaxations. Exploiting the polynomial kernel technique, we obtain a quadratic improvement of the known convergence rate by Reznick and Doherty and Wehner. Specifically, we show that the rate of convergence is no worse than \(O(d^2/\ell ^2)\) in the regime \(\ell = \Omega (d)\) where

    更新日期:2020-07-06
  • Mixed-integer optimal control under minimum dwell time constraints
    Math. Program. (IF 2.823) Pub Date : 2020-07-04
    Clemens Zeile, Nicolò Robuschi, Sebastian Sager

    Tailored Mixed-Integer Optimal Control policies for real-world applications usually have to avoid very short successive changes of the active integer control. Minimum dwell time (MDT) constraints express this requirement and can be included into the combinatorial integral approximation decomposition, which solves mixed-integer optimal control problems (MIOCPs) to \(\epsilon \)-optimality by solving

    更新日期:2020-07-05
  • Steklov convexification and a trajectory method for global optimization of multivariate quartic polynomials
    Math. Program. (IF 2.823) Pub Date : 2020-07-04
    Regina S. Burachik, C. Yalçın Kaya

    The Steklov function \(\mu _f(\cdot ,t)\) is defined to average a continuous function f at each point of its domain by using a window of size given by \(t>0\). It has traditionally been used to approximate f smoothly with small values of t. In this paper, we first find a concise and useful expression for \(\mu _f\) for the case when f is a multivariate quartic polynomial. Then we show that, for large

    更新日期:2020-07-05
  • Extended formulations from communication protocols in output-efficient time
    Math. Program. (IF 2.823) Pub Date : 2020-07-03
    Manuel Aprile, Yuri Faenza

    Deterministic protocols are well-known tools to obtain extended formulations, with many applications to polytopes arising in combinatorial optimization. Although constructive, those tools are not output-efficient, since the time needed to produce the extended formulation also depends on the number of rows of the slack matrix (hence, on the exact description in the original space). We give general sufficient

    更新日期:2020-07-03
  • Convergence rates for an inertial algorithm of gradient type associated to a smooth non-convex minimization
    Math. Program. (IF 2.823) Pub Date : 2020-07-01
    Szilárd Csaba László

    We investigate an inertial algorithm of gradient type in connection with the minimization of a non-convex differentiable function. The algorithm is formulated in the spirit of Nesterov’s accelerated convex gradient method. We prove some abstract convergence results which applied to our numerical scheme allow us to show that the generated sequences converge to a critical point of the objective function

    更新日期:2020-07-01
  • Existence of efficient and properly efficient solutions to problems of constrained vector optimization
    Math. Program. (IF 2.823) Pub Date : 2020-07-01
    Do Sang Kim, Boris S. Mordukhovich, Tiến-Sơn Phạm, Nguyen Van Tuyen

    The paper is devoted to the existence of global optimal solutions for a general class of nonsmooth problems of constrained vector optimization without boundedness assumptions on constraint set. The main attention is paid to the two major notions of optimality in vector problems: Pareto efficiency and proper efficiency in the sense of Geoffrion. Employing adequate tools of variational analysis and generalized

    更新日期:2020-07-01
  • A generic exact solver for vehicle routing and related problems
    Math. Program. (IF 2.823) Pub Date : 2020-06-25
    Artur Pessoa, Ruslan Sadykov, Eduardo Uchoa, François Vanderbeck

    Major advances were recently obtained in the exact solution of vehicle routing problems (VRPs). Sophisticated branch-cut-and-price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However, adapting and reimplementing those successful algorithms for other variants can be a very demanding task. This work proposes a BCP solver

    更新日期:2020-06-25
  • Approximate multi-matroid intersection via iterative refinement
    Math. Program. (IF 2.823) Pub Date : 2020-06-15
    André Linhares, Neil Olver, Chaitanya Swamy, Rico Zenklusen

    We introduce a new iterative rounding technique to round a point in a matroid polytope subject to further matroid constraints. This technique returns an independent set in one matroid with limited violations of the constraints of the other matroids. In addition to the classical steps of iterative relaxation approaches, we iteratively refine involved matroid constraints. This leads to more restrictive

    更新日期:2020-06-18
  • On the linear convergence rates of exchange and continuous methods for total variation minimization
    Math. Program. (IF 2.823) Pub Date : 2020-06-16
    Axel Flinth, Frédéric de Gournay, Pierre Weiss

    We analyze an exchange algorithm for the numerical solution total-variation regularized inverse problems over the space \(\mathcal {M}(\varOmega )\) of Radon measures on a subset \(\varOmega \) of \(\mathbb {R}^d\). Our main result states that under some regularity conditions, the method eventually converges linearly. Additionally, we prove that continuously optimizing the amplitudes of positions of

    更新日期:2020-06-16
  • Discrete optimization methods for group model selection in compressed sensing
    Math. Program. (IF 2.823) Pub Date : 2020-06-13
    Bubacarr Bah, Jannis Kurtz, Oliver Schaudt

    In this article we study the problem of signal recovery for group models. More precisely for a given set of groups, each containing a small subset of indices, and for given linear sketches of the true signal vector which is known to be group-sparse in the sense that its support is contained in the union of a small number of these groups, we study algorithms which successfully recover the true signal

    更新日期:2020-06-13
  • On a multistage discrete stochastic optimization problem with stochastic constraints and nested sampling
    Math. Program. (IF 2.823) Pub Date : 2020-06-12
    Thuy Anh Ta, Tien Mai, Fabian Bastin, Pierre L’Ecuyer

    We consider a multistage stochastic discrete program in which constraints on any stage might involve expectations that cannot be computed easily and are approximated by simulation. We study a sample average approximation (SAA) approach that uses nested sampling, in which at each stage, a number of scenarios are examined and a number of simulation replications are performed for each scenario to estimate

    更新日期:2020-06-12
  • New metric properties for prox-regular sets
    Math. Program. (IF 2.823) Pub Date : 2020-06-11
    S. Adly, F. Nacry, L. Thibault

    In this paper, we present diverse new metric properties that prox-regular sets shared with convex ones. At the heart of our work lie the Legendre-Fenchel transform and complements of balls. First, we show that a connected prox-regular set is completely determined by the Legendre-Fenchel transform of a suitable perturbation of its indicator function. Then, we prove that such a function is also the right

    更新日期:2020-06-11
  • Tikhonov regularization of a second order dynamical system with Hessian driven damping
    Math. Program. (IF 2.823) Pub Date : 2020-06-11
    Radu Ioan Boţ, Ernö Robert Csetnek, Szilárd Csaba László

    We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in Hilbert spaces. We obtain fast convergence results for the function values along the trajectories. The Tikhonov regularization term enables the derivation of strong

    更新日期:2020-06-11
  • Decomposition of arrow type positive semidefinite matrices with application to topology optimization
    Math. Program. (IF 2.823) Pub Date : 2020-06-11
    Michal Kočvara

    Decomposition of large matrix inequalities for matrices with chordal sparsity graph has been recently used by Kojima et al. (Math Program 129(1):33–68, 2011) to reduce problem size of large scale semidefinite optimization (SDO) problems and thus increase efficiency of standard SDO software. A by-product of such a decomposition is the introduction of new dense small-size matrix variables. We will show

    更新日期:2020-06-11
  • Optimization landscape of Tucker decomposition
    Math. Program. (IF 2.823) Pub Date : 2020-06-09
    Abraham Frandsen, Rong Ge

    Tucker decomposition is a popular technique for many data analysis and machine learning applications. Finding a Tucker decomposition is a nonconvex optimization problem. As the scale of the problems increases, local search algorithms such as stochastic gradient descent have become popular in practice. In this paper, we characterize the optimization landscape of the Tucker decomposition problem. In

    更新日期:2020-06-09
  • Finding and verifying the nucleolus of cooperative games
    Math. Program. (IF 2.823) Pub Date : 2020-06-06
    Márton Benedek, Jörg Fliege, Tri-Dung Nguyen

    The nucleolus offers a desirable payoff-sharing solution in cooperative games, thanks to its attractive properties—it always exists and lies in the core (if the core is non-empty), and it is unique. The nucleolus is considered as the most ‘stable’ solution in the sense that it lexicographically minimizes the dissatisfactions among all coalitions. Although computing the nucleolus is very challenging

    更新日期:2020-06-06
  • Random projections for quadratic programs
    Math. Program. (IF 2.823) Pub Date : 2020-06-06
    Claudia D’Ambrosio, Leo Liberti, Pierre-Louis Poirion, Ky Vu

    Random projections map a set of points in a high dimensional space to a lower dimensional one while approximately preserving all pairwise Euclidean distances. Although random projections are usually applied to numerical data, we show in this paper that they can be successfully applied to quadratic programming formulations over a set of linear inequality constraints. Instead of solving the higher-dimensional

    更新日期:2020-06-06
  • A scaling algorithm for optimizing arbitrary functions over vertices of polytopes
    Math. Program. (IF 2.823) Pub Date : 2020-06-04
    Sergei Chubanov

    In this paper we present a scaling algorithm for minimizing arbitrary functions over vertices of polytopes in an oracle model of computation which includes an augmentation oracle. For the binary case, when the vertices are 0–1 vectors, we show that the oracle time is polynomial. Also, this algorithm allows us to generalize some concepts of combinatorial optimization concerning performance bounds of

    更新日期:2020-06-04
  • Bi-perspective functions for mixed-integer fractional programs with indicator variables
    Math. Program. (IF 2.823) Pub Date : 2020-05-30
    Adam N. Letchford, Qiang Ni, Zhaoyu Zhong

    Perspective functions have long been used to convert fractional programs into convex programs. More recently, they have been used to form tight relaxations of mixed-integer nonlinear programs with so-called indicator variables. Motivated by a practical application (maximising energy efficiency in an OFDMA system), we consider problems that have a fractional objective and indicator variables simultaneously

    更新日期:2020-05-30
  • Sensitivity analysis of maximally monotone inclusions via the proto-differentiability of the resolvent operator
    Math. Program. (IF 2.823) Pub Date : 2020-05-27
    Samir Adly, R. Tyrrell Rockafellar

    This paper is devoted to the study of sensitivity to perturbation of parametrized variational inclusions involving maximally monotone operators in a Hilbert space. The perturbation of all the data involved in the problem is taken into account. Using the concept of proto-differentiability of a multifunction and the notion of semi-differentiability of a single-valued map, we establish the differentiability

    更新日期:2020-05-27
  • A computational study of exact subgraph based SDP bounds for Max-Cut, stable set and coloring.
    Math. Program. (IF 2.823) Pub Date : 2020-05-25
    Elisabeth Gaar,Franz Rendl

    The “exact subgraph” approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational challenge because of the potentially large number of violated subgraph constraints. We introduce a computational framework for these relaxations designed to cope with

    更新日期:2020-05-25
  • Sparse semidefinite programs with guaranteed near-linear time complexity via dualized clique tree conversion
    Math. Program. (IF 2.823) Pub Date : 2020-05-25
    Richard Y. Zhang, Javad Lavaei

    Clique tree conversion solves large-scale semidefinite programs by splitting an \(n\times n\) matrix variable into up to n smaller matrix variables, each representing a principal submatrix of up to \(\omega \times \omega \). Its fundamental weakness is the need to introduce overlap constraints that enforce agreement between different matrix variables, because these can result in dense coupling. In

    更新日期:2020-05-25
  • Maximum edge-disjoint paths in planar graphs with congestion 2
    Math. Program. (IF 2.823) Pub Date : 2020-05-20
    Loïc Séguin-Charbonneau, F. Bruce Shepherd

    We study the maximum edge-disjoint path problem (medp) in planar graphs \(G=(V,E)\) with edge capacities u(e). We are given a set of terminal pairs \(s_it_i\), \(i=1,2 \ldots , k\) and wish to find a maximum routable subset of demands. That is, a subset of demands that can be connected by a family of paths that use each edge at most u(e) times. It is well-known that there is an integrality gap of \(\Omega

    更新日期:2020-05-20
  • Box-total dual integrality, box-integrality, and equimodular matrices
    Math. Program. (IF 2.823) Pub Date : 2020-05-20
    Patrick Chervet, Roland Grappe, Louis-Hadrien Robert

    Box-totally dual integral (box-TDI) polyhedra are polyhedra described by systems which yield strong min-max relations. We characterize them in several ways, involving the notions of principal box-integer polyhedra and equimodular matrices. A polyhedron is box-integer if its intersection with any integer box \(\{\ell \le x \le u\}\) is integer. We define principally box-integer polyhedra to be the polyhedra P

    更新日期:2020-05-20
  • An exact algorithm for robust influence maximization
    Math. Program. (IF 2.823) Pub Date : 2020-05-19
    Giacomo Nannicini, Giorgio Sartor, Emiliano Traversi, Roberto Wolfler Calvo

    We propose a Branch-and-Cut algorithm for the robust influence maximization problem. The influence maximization problem aims to identify, in a social network, a set of given cardinality comprising actors that are able to influence the maximum number of other actors. We assume that the social network is given in the form of a graph with node thresholds to indicate the resistance of an actor to influence

    更新日期:2020-05-19
  • Breaking symmetries to rescue sum of squares in the case of makespan scheduling
    Math. Program. (IF 2.823) Pub Date : 2020-05-14
    Victor Verdugo, José Verschae, Andreas Wiese

    The sum of squares (SoS) hierarchy gives an automatized technique to create a family of increasingly tight convex relaxations for binary programs. There are several problems for which a constant number of rounds of this hierarchy give integrality gaps matching the best known approximation algorithms. For many other problems, however, ad-hoc techniques give better approximation ratios than SoS in the

    更新日期:2020-05-14
  • Adaptive regularization with cubics on manifolds
    Math. Program. (IF 2.823) Pub Date : 2020-05-13
    Naman Agarwal, Nicolas Boumal, Brian Bullins, Coralia Cartis

    Adaptive regularization with cubics (ARC) is an algorithm for unconstrained, non-convex optimization. Akin to the trust-region method, its iterations can be thought of as approximate, safe-guarded Newton steps. For cost functions with Lipschitz continuous Hessian, ARC has optimal iteration complexity, in the sense that it produces an iterate with gradient smaller than \(\varepsilon \) in \(O(1/\varepsilon

    更新日期:2020-05-13
  • Stochastic quasi-gradient methods: variance reduction via Jacobian sketching
    Math. Program. (IF 2.823) Pub Date : 2020-05-12
    Robert M. Gower, Peter Richtárik, Francis Bach

    We develop a new family of variance reduced stochastic gradient descent methods for minimizing the average of a very large number of smooth functions. Our method—JacSketch—is motivated by novel developments in randomized numerical linear algebra, and operates by maintaining a stochastic estimate of a Jacobian matrix composed of the gradients of individual functions. In each iteration, JacSketch efficiently

    更新日期:2020-05-12
  • The condition number of a function relative to a set
    Math. Program. (IF 2.823) Pub Date : 2020-05-06
    David H. Gutman, Javier F. Peña

    The condition number of a differentiable convex function, namely the ratio of its smoothness to strong convexity constants, is closely tied to fundamental properties of the function. In particular, the condition number of a quadratic convex function is the square of the aspect ratio of a canonical ellipsoid associated to the function. Furthermore, the condition number of a function bounds the linear

    更新日期:2020-05-06
  • Dynamic flows with adaptive route choice
    Math. Program. (IF 2.823) Pub Date : 2020-05-04
    Lukas Graf, Tobias Harks, Leon Sering

    We study dynamic network flows and introduce a notion of instantaneous dynamic equilibrium (IDE) requiring that for any positive inflow into an edge, this edge must lie on a currently shortest path towards the respective sink. We measure current shortest path length by current waiting times in queues plus physical travel times. As our main results, we show: 1. existence and constructive computation

    更新日期:2020-05-04
  • Strong formulations for conic quadratic optimization with indicator variables
    Math. Program. (IF 2.823) Pub Date : 2020-04-30
    Andrés Gómez

    We study the convex hull of the mixed-integer set given by a conic quadratic inequality and indicator variables. Conic quadratic terms are often used to encode uncertainties, while the indicator variables are used to model fixed costs or enforce sparsity in the solutions. We provide the convex hull description of the set under consideration when the continuous variables are unbounded. We propose valid

    更新日期:2020-04-30
  • Separation routine and extended formulations for the stable set problem in claw-free graphs
    Math. Program. (IF 2.823) Pub Date : 2020-04-28
    Yuri Faenza, Gianpaolo Oriolo, Gautier Stauffer

    The maximum weighted stable set problem in claw-free graphs is a well-known generalization of the maximum weighted matching problem, and a classical problem in combinatorial optimization. In spite of the recent development of fast(er) combinatorial algorithms and some progresses in the characterization of the corresponding stable set polytope, the problem of “providing a decent linear description”

    更新日期:2020-04-28
  • An efficient characterization of submodular spanning tree games.
    Math. Program. (IF 2.823) Pub Date : 2020-04-25
    Zhuan Khye Koh,Laura Sanità

    Cooperative games form an important class of problems in game theory, where a key goal is to distribute a value among a set of players who are allowed to cooperate by forming coalitions. An outcome of the game is given by an allocation vector that assigns a value share to each player. A crucial aspect of such games is submodularity (or convexity). Indeed, convex instances of cooperative games exhibit

    更新日期:2020-04-25
  • Simple bilevel programming and extensions
    Math. Program. (IF 2.823) Pub Date : 2020-04-25
    Stephan Dempe, Nguyen Dinh, Joydeep Dutta, Tanushree Pandit

    In this paper we discuss the simple bilevel programming problem (SBP) and its extension, the simple mathematical programming problem under equilibrium constraints (SMPEC). Here we first define both these problems and study their interrelations. Next we study the various types of necessary and sufficient optimality conditions for the (SMPEC) problems, which occur under various reformulations. The optimality

    更新日期:2020-04-25
  • Generalized monotone operators and their averaged resolvents
    Math. Program. (IF 2.823) Pub Date : 2020-04-25
    Heinz H. Bauschke, Walaa M. Moursi, Xianfu Wang

    The correspondence between the monotonicity of a (possibly) set-valued operator and the firm nonexpansiveness of its resolvent is a key ingredient in the convergence analysis of many optimization algorithms. Firmly nonexpansive operators form a proper subclass of the more general—but still pleasant from an algorithmic perspective—class of averaged operators. In this paper, we introduce the new notion

    更新日期:2020-04-25
  • Revenue maximization in Stackelberg Pricing Games: beyond the combinatorial setting
    Math. Program. (IF 2.823) Pub Date : 2020-04-18
    Toni Böhnlein, Stefan Kratsch, Oliver Schaudt

    In a Stackelberg Pricing Game a distinguished player, the leader, chooses prices for a set of items, and the other players, the followers, each seek to buy a minimum cost feasible subset of the items. The goal of the leader is to maximize her revenue, which is determined by the sold items and their prices. Most previously studied cases of such games can be captured by a combinatorial model where we

    更新日期:2020-04-22
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