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  • 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
  • Conservative set valued fields, automatic differentiation, stochastic gradient methods and deep learning
    Math. Program. (IF 2.823) Pub Date : 2020-04-15
    Jérôme Bolte, Edouard Pauwels

    Modern problems in AI or in numerical analysis require nonsmooth approaches with a flexible calculus. We introduce generalized derivatives called conservative fields for which we develop a calculus and provide representation formulas. Functions having a conservative field are called path differentiable: convex, concave, Clarke regular and any semialgebraic Lipschitz continuous functions are path differentiable

    更新日期:2020-04-22
  • A new contraction technique with applications to congruency-constrained cuts
    Math. Program. (IF 2.823) Pub Date : 2020-04-15
    Martin Nägele, Rico Zenklusen

    Minimum cut problems are among the most classical problems in Combinatorial Optimization and are used in a wide set of applications. Some of the best-known efficiently solvable variants include global mininmum cuts, minimum s–t cuts, and minimum odd cuts in undirected graphs. We study a problem class that can be seen to generalize the above variants, namely finding congruency-constrained minimum cuts

    更新日期:2020-04-22
  • Better and simpler error analysis of the Sinkhorn–Knopp algorithm for matrix scaling
    Math. Program. (IF 2.823) Pub Date : 2020-04-15
    Deeparnab Chakrabarty, Sanjeev Khanna

    Given a non-negative \(n \times m\) real matrix A, the matrix scaling problem is to determine if it is possible to scale the rows and columns so that each row and each column sums to a specified positive target values. The Sinkhorn–Knopp algorithm is a simple and classic procedure which alternately scales all rows and all columns to meet these targets. The focus of this paper is the worst-case theoretical

    更新日期:2020-04-22
  • Complexity of packing common bases in matroids
    Math. Program. (IF 2.823) Pub Date : 2020-04-08
    Kristóf Bérczi, Tamás Schwarcz

    One of the most intriguing unsolved questions of matroid optimization is the characterization of the existence of k disjoint common bases of two matroids. The significance of the problem is well-illustrated by the long list of conjectures that can be formulated as special cases, such as Woodall’s conjecture on packing disjoint dijoins in a directed graph, or Rota’s beautiful conjecture on rearrangements

    更新日期:2020-04-22
  • Duality for constrained robust sum optimization problems
    Math. Program. (IF 2.823) Pub Date : 2020-04-08
    N. Dinh, M. A. Goberna, D. H. Long, M. Volle

    Given an infinite family of extended real-valued functions \(f_{i}\), \(i\in I,\) and a family \({\mathcal {H}}\) of nonempty finite subsets of I, the \({\mathcal {H}}\)-partial robust sum of \(f_{i}\), \(i\in I,\) is the supremum, for \(J\in {\mathcal {H}},\) of the finite sums \(\sum _{j\in J}f_{j}\). These infinite sums arise in a natural way in location problems as well as in functional approximation

    更新日期:2020-04-22
  • Unit stepsize for the Newton method close to critical solutions
    Math. Program. (IF 2.823) Pub Date : 2020-04-07
    A. Fischer, A. F. Izmailov, M. V. Solodov

    As is well known, when initialized close to a nonsingular solution of a smooth nonlinear equation, the Newton method converges to this solution superlinearly. Moreover, the common Armijo linesearch procedure used to globalize the process for convergence from arbitrary starting points, accepts the unit stepsize asymptotically and ensures fast local convergence. In the case of a singular and possibly

    更新日期:2020-04-22
  • Convergent upper bounds in global minimization with nonlinear equality constraints
    Math. Program. (IF 2.823) Pub Date : 2020-04-06
    Christian Füllner, Peter Kirst, Oliver Stein

    We address the problem of determining convergent upper bounds in continuous non-convex global minimization of box-constrained problems with equality constraints. These upper bounds are important for the termination of spatial branch-and-bound algorithms. Our method is based on the theorem of Miranda which helps to ensure the existence of feasible points in certain boxes. Then, the computation of upper

    更新日期:2020-04-22
  • Inexact stochastic mirror descent for two-stage nonlinear stochastic programs
    Math. Program. (IF 2.823) Pub Date : 2020-04-02
    Vincent Guigues

    We introduce an inexact variant of stochastic mirror descent (SMD), called inexact stochastic mirror descent (ISMD), to solve nonlinear two-stage stochastic programs where the second stage problem has linear and nonlinear coupling constraints and a nonlinear objective function which depends on both first and second stage decisions. Given a candidate first stage solution and a realization of the second

    更新日期:2020-04-22
  • Regional complexity analysis of algorithms for nonconvex smooth optimization
    Math. Program. (IF 2.823) Pub Date : 2020-04-01
    Frank E. Curtis, Daniel P. Robinson

    A strategy is proposed for characterizing the worst-case performance of algorithms for solving nonconvex smooth optimization problems. Contemporary analyses characterize worst-case performance by providing, under certain assumptions on an objective function, an upper bound on the number of iterations (or function or derivative evaluations) required until a pth-order stationarity condition is approximately

    更新日期:2020-04-22
  • Symmetry-breaking inequalities for ILP with structured sub-symmetry
    Math. Program. (IF 2.823) Pub Date : 2020-03-30
    Pascale Bendotti, Pierre Fouilhoux, Cécile Rottner

    We consider integer linear programs whose solutions are binary matrices and whose (sub-)symmetry groups are symmetric groups acting on (sub-)columns. Such structured sub-symmetry groups arise in important classes of combinatorial problems, e.g. graph coloring or unit commitment. For a priori known (sub-)symmetries, we propose a framework to build (sub-)symmetry-breaking inequalities for such problems

    更新日期:2020-04-22
  • A sequential homotopy method for mathematical programming problems
    Math. Program. (IF 2.823) Pub Date : 2020-03-23
    Andreas Potschka, Hans Georg Bock

    We propose a sequential homotopy method for the solution of mathematical programming problems formulated in abstract Hilbert spaces under the Guignard constraint qualification. The method is equivalent to performing projected backward Euler timestepping on a projected gradient/antigradient flow of the augmented Lagrangian. The projected backward Euler equations can be interpreted as the necessary optimality

    更新日期:2020-04-22
  • Analysis of biased stochastic gradient descent using sequential semidefinite programs
    Math. Program. (IF 2.823) Pub Date : 2020-03-23
    Bin Hu, Peter Seiler, Laurent Lessard

    We present a convergence rate analysis for biased stochastic gradient descent (SGD), where individual gradient updates are corrupted by computation errors. We develop stochastic quadratic constraints to formulate a small linear matrix inequality (LMI) whose feasible points lead to convergence bounds of biased SGD. Based on this LMI condition, we develop a sequential minimization approach to analyze

    更新日期:2020-04-22
  • Dynamic stochastic approximation for multi-stage stochastic optimization
    Math. Program. (IF 2.823) Pub Date : 2020-03-20
    Guanghui Lan, Zhiqiang Zhou

    In this paper, we consider multi-stage stochastic optimization problems with convex objectives and conic constraints at each stage. We present a new stochastic first-order method, namely the dynamic stochastic approximation (DSA) algorithm, for solving these types of stochastic optimization problems. We show that DSA can achieve an optimal \({{\mathcal {O}}}(1/\epsilon ^4)\) rate of convergence in

    更新日期:2020-04-22
  • Distributed stochastic gradient tracking methods
    Math. Program. (IF 2.823) Pub Date : 2020-03-17
    Shi Pu, Angelia Nedić

    In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that minimizes the average of all cost functions. Assuming agents only have access to unbiased estimates of the gradients of their local cost functions, we consider a distributed

    更新日期:2020-04-22
  • Improving the integrality gap for multiway cut
    Math. Program. (IF 2.823) Pub Date : 2020-03-06
    Kristóf Bérczi, Karthekeyan Chandrasekaran, Tamás Király, Vivek Madan

    In the multiway cut problem, we are given an undirected graph with non-negative edge weights and a collection of k terminal nodes, and the goal is to partition the node set of the graph into k non-empty parts each containing exactly one terminal, so that the total weight of the edges crossing the partition is minimized. The multiway cut problem for \(k\ge 3\) is APX-hard. For arbitrary k, the best-known

    更新日期:2020-04-22
  • Generalized stochastic Frank–Wolfe algorithm with stochastic “substitute” gradient for structured convex optimization
    Math. Program. (IF 2.823) Pub Date : 2020-03-04
    Haihao Lu, Robert M. Freund

    The stochastic Frank–Wolfe method has recently attracted much general interest in the context of optimization for statistical and machine learning due to its ability to work with a more general feasible region. However, there has been a complexity gap in the dependence on the optimality tolerance \(\varepsilon \) in the guaranteed convergence rate for stochastic Frank–Wolfe compared to its deterministic

    更新日期:2020-04-22
  • Varying confidence levels for CVaR risk measures and minimax limits
    Math. Program. (IF 2.823) Pub Date : 2019-01-22
    Edward Anderson, Huifu Xu, Dali Zhang

    Conditional value at risk (CVaR) has been widely studied as a risk measure. In this paper we add to this work by focusing on the choice of confidence level and its impact on optimization problems with CVaR appearing in the objective and also the constraints. We start by considering a problem in which CVaR is minimized and investigate the way in which it approximates the minimax robust optimization

    更新日期:2020-04-22
  • Using regularization and second order information in outer approximation for convex MINLP
    Math. Program. (IF 2.823) Pub Date : 2018-12-18
    Jan Kronqvist, David E. Bernal, Ignacio E. Grossmann

    In this paper, we present two new methods for solving convex mixed-integer nonlinear programming problems based on the outer approximation method. The first method is inspired by the level method and uses a regularization technique to reduce the step size when choosing new integer combinations. The second method combines ideas from both the level method and the sequential quadratic programming technique

    更新日期:2020-04-22
  • Piecewise affine parameterized value-function based bilevel non-cooperative games
    Math. Program. (IF 2.823) Pub Date : 2018-11-10
    Tianyu Hao, Jong-Shi Pang

    Generalizing certain network interdiction games communicated to us by Andrew Liu and his collaborators, this paper studies a bilevel, non-cooperative game wherein the objective function of each player’s optimization problem contains a value function of a second-level linear program parameterized by the first-level variables in a non-convex manner. In the applied network interdiction games, this parameterization

    更新日期:2020-04-22
  • Optimality conditions and global convergence for nonlinear semidefinite programming
    Math. Program. (IF 2.823) Pub Date : 2018-12-07
    Roberto Andreani, Gabriel Haeser, Daiana S. Viana

    Abstract Sequential optimality conditions have played a major role in unifying and extending global convergence results for several classes of algorithms for general nonlinear optimization. In this paper, we extend theses concepts for nonlinear semidefinite programming. We define two sequential optimality conditions for nonlinear semidefinite programming. The first is a natural extension of the so-called

    更新日期:2020-03-20
  • Balas formulation for the union of polytopes is optimal
    Math. Program. (IF 2.823) Pub Date : 2019-01-19
    Michele Conforti, Marco Di Summa, Yuri Faenza

    Abstract A celebrated theorem of Balas gives a linear mixed-integer formulation for the union of two nonempty polytopes whose relaxation gives the convex hull of this union. The number of inequalities in Balas formulation is linear in the number of inequalities that describe the two polytopes and the number of variables is doubled. In this paper we show that this is best possible: in every dimension

    更新日期:2020-03-20
  • Convergence rate of inertial Forward–Backward algorithm beyond Nesterov’s rule
    Math. Program. (IF 2.823) Pub Date : 2018-11-12
    Vassilis Apidopoulos, Jean-François Aujol, Charles Dossal

    Abstract In this paper we study the convergence of an Inertial Forward–Backward algorithm, with a particular choice of an over-relaxation term. In particular we show that for a sequence of over-relaxation parameters, that do not satisfy Nesterov’s rule, one can still expect some relatively fast convergence properties for the objective function. In addition we complement this work by studying the convergence

    更新日期:2020-03-20
  • Faster subgradient methods for functions with Hölderian growth
    Math. Program. (IF 2.823) Pub Date : 2019-01-07
    Patrick R. Johnstone, Pierre Moulin

    Abstract The purpose of this manuscript is to derive new convergence results for several subgradient methods applied to minimizing nonsmooth convex functions with Hölderian growth. The growth condition is satisfied in many applications and includes functions with quadratic growth and weakly sharp minima as special cases. To this end there are three main contributions. First, for a constant and sufficiently

    更新日期:2020-03-20
  • A Newton-CG algorithm with complexity guarantees for smooth unconstrained optimization
    Math. Program. (IF 2.823) Pub Date : 2019-01-19
    Clément W. Royer, Michael O’Neill, Stephen J. Wright

    Abstract We consider minimization of a smooth nonconvex objective function using an iterative algorithm based on Newton’s method and the linear conjugate gradient algorithm, with explicit detection and use of negative curvature directions for the Hessian of the objective function. The algorithm tracks Newton-conjugate gradient procedures developed in the 1980s closely, but includes enhancements that

    更新日期:2020-03-20
  • Second-order variational analysis in second-order cone programming
    Math. Program. (IF 2.823) Pub Date : 2018-11-03
    Nguyen T. V. Hang, Boris S. Mordukhovich, M. Ebrahim Sarabi

    Abstract The paper conducts a second-order variational analysis for an important class of nonpolyhedral conic programs generated by the so-called second-order/Lorentz/ice-cream cone \({\mathcal {Q}}\). From one hand, we prove that the indicator function of \({\mathcal {Q}}\) is always twice epi-differentiable and apply this result to characterizing the uniqueness of Lagrange multipliers together with

    更新日期:2020-03-20
  • New analysis of linear convergence of gradient-type methods via unifying error bound conditions
    Math. Program. (IF 2.823) Pub Date : 2019-01-04
    Hui Zhang

    Abstract This paper reveals that a common and central role, played in many error bound (EB) conditions and a variety of gradient-type methods, is a residual measure operator. On one hand, by linking this operator with other optimality measures, we define a group of abstract EB conditions, and then analyze the interplay between them; on the other hand, by using this operator as an ascent direction,

    更新日期:2020-03-20
  • Network strength games: the core and the nucleolus
    Math. Program. (IF 2.823) Pub Date : 2018-11-09
    Mourad Baïou, Francisco Barahona

    Abstract The maximum number of edge-disjoint spanning trees in a network has been used as a measure of the strength of a network. It gives the number of disjoint ways that the network can be fully connected. This suggests a game theoretic analysis that shows the relative importance of the different links to form a strong network. We introduce the Network strength game as a cooperative game defined

    更新日期:2020-03-20
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