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  • Subregular recourse in nonlinear multistage stochastic optimization
    Math. Program. (IF 2.823) Pub Date : 2021-01-13
    Darinka Dentcheva, Andrzej Ruszczyński

    We consider nonlinear multistage stochastic optimization problems in the spaces of integrable functions. We allow for nonlinear dynamics and general objective functionals, including dynamic risk measures. We study causal operators describing the dynamics of the system and derive the Clarke subdifferential for a penalty function involving such operators. Then we introduce the concept of subregular recourse

    更新日期:2021-01-13
  • Block-coordinate and incremental aggregated proximal gradient methods for nonsmooth nonconvex problems
    Math. Program. (IF 2.823) Pub Date : 2021-01-13
    Puya Latafat, Andreas Themelis, Panagiotis Patrinos

    This paper analyzes block-coordinate proximal gradient methods for minimizing the sum of a separable smooth function and a (nonseparable) nonsmooth function, both of which are allowed to be nonconvex. The main tool in our analysis is the forward-backward envelope, which serves as a particularly suitable continuous and real-valued Lyapunov function. Global and linear convergence results are established

    更新日期:2021-01-13
  • First-order inertial algorithms involving dry friction damping
    Math. Program. (IF 2.823) Pub Date : 2021-01-13
    Samir Adly, Hedy Attouch

    In a Hilbert space \( {\mathcal H}\), we introduce a new class of first-order algorithms which naturally occur as discrete temporal versions of an inertial differential inclusion jointly involving viscous friction and dry friction. The function \(f:{\mathcal H}\rightarrow {\mathbb {R}}\) to be minimized is supposed to be differentiable (not necessarily convex), and enters the algorithm via its gradient

    更新日期:2021-01-13
  • Persistency of linear programming relaxations for the stable set problem
    Math. Program. (IF 2.823) Pub Date : 2021-01-11
    Elisabeth Rodríguez-Heck, Karl Stickler, Matthias Walter, Stefan Weltge

    The Nemhauser–Trotter theorem states that the standard linear programming (LP) formulation for the stable set problem has a remarkable property, also known as (weak) persistency: for every optimal LP solution that assigns integer values to some variables, there exists an optimal integer solution in which these variables retain the same values. While the standard LP is defined by only non-negativity

    更新日期:2021-01-11
  • Subcontracting and lot-sizing with constant capacities
    Math. Program. (IF 2.823) Pub Date : 2021-01-08
    Hark-Chin Hwang

    In this paper, we consider the subcontracting and single-item lot-sizing problem with constant capacities, which is uncapacitated in subcontracting but capacitated in production. For a holistic understanding of the problem, an infinite-period model is proposed. Such a model provides a unified view of a capacitated lot-sizing problem. The usefulness of the infinite-period model is shown by the principle

    更新日期:2021-01-08
  • On the tightness of SDP relaxations of QCQPs
    Math. Program. (IF 2.823) Pub Date : 2021-01-07
    Alex L. Wang, Fatma Kılınç-Karzan

    Quadratically constrained quadratic programs (QCQPs) are a fundamental class of optimization problems well-known to be NP-hard in general. In this paper we study conditions under which the standard semidefinite program (SDP) relaxation of a QCQP is tight. We begin by outlining a general framework for proving such sufficient conditions. Then using this framework, we show that the SDP relaxation is tight

    更新日期:2021-01-08
  • Local convergence of tensor methods
    Math. Program. (IF 2.823) Pub Date : 2021-01-04
    Nikita Doikov, Yurii Nesterov

    In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumption of uniform convexity of the smooth component, having Lipschitz-continuous high-order derivative. The convergence both in function value and in the norm of minimal subgradient is established. Global complexity

    更新日期:2021-01-05
  • A hybrid stochastic optimization framework for composite nonconvex optimization
    Math. Program. (IF 2.823) Pub Date : 2021-01-04
    Quoc Tran-Dinh, Nhan H. Pham, Dzung T. Phan, Lam M. Nguyen

    We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine a variance-reduced estimator and an unbiased stochastic one to create a new hybrid estimator which trades-off the variance and bias, and possesses useful properties for developing new algorithms. We first introduce our

    更新日期:2021-01-05
  • Mixing convex-optimization bounds for maximum-entropy sampling
    Math. Program. (IF 2.823) Pub Date : 2021-01-04
    Zhongzhu Chen, Marcia Fampa, Amélie Lambert, Jon Lee

    The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-s principal submatrix of an order-n covariance matrix. Exact solution methods for this NP-hard problem are based on a branch-and-bound framework. Many of the known upper bounds for the optimal value are based on

    更新日期:2021-01-05
  • Subdifferential of the supremum function: moving back and forth between continuous and non-continuous settings
    Math. Program. (IF 2.823) Pub Date : 2020-11-27
    R. Correa, A. Hantoute, M. A. López

    In this paper we establish general formulas for the subdifferential of the pointwise supremum of convex functions, which cover and unify both the compact continuous and the non-compact non-continuous settings. From the non-continuous to the continuous setting, we proceed by a compactification-based approach which leads us to problems having compact index sets and upper semi-continuously indexed mappings

    更新日期:2020-11-27
  • Compactness and convergence rates in the combinatorial integral approximation decomposition
    Math. Program. (IF 2.823) Pub Date : 2020-11-25
    Christian Kirches, Paul Manns, Stefan Ulbrich

    The combinatorial integral approximation decomposition splits the optimization of a discrete-valued control into two steps: solving a continuous relaxation of the discrete control problem, and computing a discrete-valued approximation of the relaxed control. Different algorithms exist for the second step to construct piecewise constant discrete-valued approximants that are defined on given decompositions

    更新日期:2020-11-25
  • Doubly nonnegative relaxations for quadratic and polynomial optimization problems with binary and box constraints
    Math. Program. (IF 2.823) Pub Date : 2020-11-21
    Sunyoung Kim, Masakazu Kojima, Kim-Chuan Toh

    We propose a doubly nonnegative (DNN) relaxation for polynomial optimization problems (POPs) with binary and box constraints. This work is an extension of the work by Kim, Kojima and Toh in 2016 from quadratic optimization problems to POPs. The dense and sparse DNN relaxations are reduced to a simple conic optimization problem (COP) to which an accelerated bisection and projection (BP) algorithm is

    更新日期:2020-11-22
  • Role of sparsity and structure in the optimization landscape of non-convex matrix sensing
    Math. Program. (IF 2.823) Pub Date : 2020-11-20
    Igor Molybog, Somayeh Sojoudi, Javad Lavaei

    In this work, we study the optimization landscape of the non-convex matrix sensing problem that is known to have many local minima in the worst case. Since the existing results are related to the notion of restricted isometry property (RIP) that cannot directly capture the underlying structure of a given problem, they can hardly be applied to real-world problems where the amount of data is not exorbitantly

    更新日期:2020-11-21
  • Asymptotic behavior of integer programming and the stability of the Castelnuovo–Mumford regularity
    Math. Program. (IF 2.823) Pub Date : 2020-11-19
    Le Tuan Hoa

    The paper provides a connection between Commutative Algebra and Integer Programming and contains two parts. The first one is devoted to the asymptotic behavior of integer programs with a fixed cost linear functional and the constraint sets consisting of a finite system of linear equations or inequalities with integer coefficients depending linearly on n. An integer \(N_*\) is determined such that the

    更新日期:2020-11-19
  • A unified concept of approximate and quasi efficient solutions and associated subdifferentials in multiobjective optimization
    Math. Program. (IF 2.823) Pub Date : 2020-11-18
    L. Huerga, B. Jiménez, D. T. Luc, V. Novo

    In this paper, we introduce some new notions of quasi efficiency and quasi proper efficiency for multiobjective optimization problems that reduce to the most important concepts of approximate and quasi efficient solutions given up to now. We establish main properties and provide characterizations for these solutions by linear and nonlinear scalarizations. With the help of quasi efficient solutions

    更新日期:2020-11-18
  • Quantum entanglement, symmetric nonnegative quadratic polynomials and moment problems
    Math. Program. (IF 2.823) Pub Date : 2020-11-17
    Grigoriy Blekherman, Bharath Hebbe Madhusudhana

    Quantum states are represented by positive semidefinite Hermitian operators with unit trace, known as density matrices. An important subset of quantum states is that of separable states, the complement of which is the subset of entangled states. We show that the problem of deciding whether a quantum state is entangled can be seen as a moment problem in real analysis. Only a small number of such moments

    更新日期:2020-11-17
  • First-order optimization algorithms via inertial systems with Hessian driven damping
    Math. Program. (IF 2.823) Pub Date : 2020-11-16
    Hedy Attouch, Zaki Chbani, Jalal Fadili, Hassan Riahi

    In a Hilbert space setting, for convex optimization, we analyze the convergence rate of a class of first-order algorithms involving inertial features. They can be interpreted as discrete time versions of inertial dynamics involving both viscous and Hessian-driven dampings. The geometrical damping driven by the Hessian intervenes in the dynamics in the form \(\nabla ^2 f (x(t)) \dot{x} (t)\). By treating

    更新日期:2020-11-16
  • Dynamic probabilistic constraints under continuous random distributions
    Math. Program. (IF 2.823) Pub Date : 2020-11-13
    T. González Grandón, R. Henrion, P. Pérez-Aros

    The paper investigates analytical properties of dynamic probabilistic constraints (chance constraints). The underlying random distribution is supposed to be continuous. In the first part, a general multistage model with decision rules depending on past observations of the random process is analyzed. Basic properties like (weak sequential) (semi-) continuity of the probability function or existence

    更新日期:2020-11-15
  • Idealness of k -wise intersecting families
    Math. Program. (IF 2.823) Pub Date : 2020-11-11
    Ahmad Abdi, Gérard Cornuéjols, Tony Huynh, Dabeen Lee

    A clutter is k-wise intersecting if every k members have a common element, yet no element belongs to all members. We conjecture that, for some integer \(k\ge 4\), every k-wise intersecting clutter is non-ideal. As evidence for our conjecture, we prove it for \(k=4\) for the class of binary clutters. Two key ingredients for our proof are Jaeger’s 8-flow theorem for graphs, and Seymour’s characterization

    更新日期:2020-11-12
  • A tight degree 4 sum-of-squares lower bound for the Sherrington–Kirkpatrick Hamiltonian
    Math. Program. (IF 2.823) Pub Date : 2020-11-05
    Dmitriy Kunisky, Afonso S. Bandeira

    We show that, if \({\varvec{W}}\) is an \(N \times N\) matrix drawn from the gaussian orthogonal ensemble, then with high probability the degree 4 sum-of-squares relaxation cannot certify an upper bound on the objective \(N^{-1} \cdot \varvec{x}^\top \varvec{W} \varvec{x}\) under the constraints \(x_i^2 - 1 = 0\) (i.e. \(\varvec{x}\in \{\pm 1 \}^N\)) that is asymptotically smaller than \(\lambda _{\max

    更新日期:2020-11-05
  • Nonnegative forms with sublevel sets of minimal volume
    Math. Program. (IF 2.823) Pub Date : 2020-11-03
    Khazhgali Kozhasov, Jean Bernard Lasserre

    We show that the Euclidean ball has the smallest volume among sublevel sets of nonnegative forms of bounded Bombieri norm as well as among sublevel sets of sum of squares forms whose Gram matrix has bounded Frobenius or nuclear (or, more generally, p-Schatten) norm. These volume-minimizing properties of the Euclidean ball with respect to its representation (as a sublevel set of a form of fixed even

    更新日期:2020-11-03
  • Smoothed analysis for tensor methods in unsupervised learning
    Math. Program. (IF 2.823) Pub Date : 2020-11-02
    Aditya Bhaskara, Aidao Chen, Aidan Perreault, Aravindan Vijayaraghavan

    Smoothed analysis is a powerful paradigm in overcoming worst-case intractability in high-dimensional data analysis and unsupervised learning. While polynomial time smoothed analysis guarantees have been obtained for worst-case intractable problems like tensor decomposition and learning mixtures of Gaussians, such guarantees have been hard to obtain for several other important problems in data analysis

    更新日期:2020-11-02
  • Near-optimal analysis of Lasserre’s univariate measure-based bounds for multivariate polynomial optimization
    Math. Program. (IF 2.823) Pub Date : 2020-10-30
    Lucas Slot, Monique Laurent

    We consider a hierarchy of upper approximations for the minimization of a polynomial f over a compact set \(K \subseteq \mathbb {R}^n\) proposed recently by Lasserre (arXiv:1907.097784, 2019). This hierarchy relies on using the push-forward measure of the Lebesgue measure on K by the polynomial f and involves univariate sums of squares of polynomials with growing degrees 2r. Hence it is weaker, but

    更新日期:2020-10-30
  • Stochastic Lipschitz dynamic programming
    Math. Program. (IF 2.823) Pub Date : 2020-10-28
    Shabbir Ahmed, Filipe Goulart Cabral, Bernardo Freitas Paulo da Costa

    We propose a new algorithm for solving multistage stochastic mixed integer linear programming (MILP) problems with complete continuous recourse. In a similar way to cutting plane methods, we construct nonlinear Lipschitz cuts to build lower approximations for the non-convex cost-to-go functions. An example of such a class of cuts are those derived using Augmented Lagrangian Duality for MILPs. The family

    更新日期:2020-10-30
  • The greedy strategy for optimizing the Perron eigenvalue
    Math. Program. (IF 2.823) Pub Date : 2020-10-27
    Aleksandar Cvetković, Vladimir Yu. Protasov

    We address the problems of minimizing and of maximizing the spectral radius over a compact family of non-negative matrices. Those problems being hard in general can be efficiently solved for some special families. We consider the so-called product families, where each matrix is composed of rows chosen independently from given sets. A recently introduced greedy method works very fast. However, it is

    更新日期:2020-10-30
  • On the optimization landscape of tensor decompositions
    Math. Program. (IF 2.823) Pub Date : 2020-10-24
    Rong Ge, Tengyu Ma

    Non-convex optimization with local search heuristics has been widely used in machine learning, achieving many state-of-art results. It becomes increasingly important to understand why they can work for these NP-hard problems on typical data. The landscape of many objective functions in learning has been conjectured to have the geometric property that “all local optima are (approximately) global optima”

    更新日期:2020-10-30
  • Mixed-integer optimal control problems with switching costs: a shortest path approach
    Math. Program. (IF 2.823) Pub Date : 2020-10-24
    Felix Bestehorn, Christoph Hansknecht, Christian Kirches, Paul Manns

    We investigate an extension of Mixed-Integer Optimal Control Problems by adding switching costs, which enables the penalization of chattering and extends current modeling capabilities. The decomposition approach, consisting of solving a partial outer convexification to obtain a relaxed solution and using rounding schemes to obtain a discrete-valued control can still be applied, but the rounding turns

    更新日期:2020-10-30
  • General bounds for incremental maximization
    Math. Program. (IF 2.823) Pub Date : 2020-10-20
    Aaron Bernstein, Yann Disser, Martin Groß, Sandra Himburg

    We propose a theoretical framework to capture incremental solutions to cardinality constrained maximization problems. The defining characteristic of our framework is that the cardinality/support of the solution is bounded by a value \(k\in {\mathbb {N}}\) that grows over time, and we allow the solution to be extended one element at a time. We investigate the best-possible competitive ratio of such

    更新日期:2020-10-20
  • Continuous cubic formulations for cluster detection problems in networks
    Math. Program. (IF 2.823) Pub Date : 2020-10-16
    Vladimir Stozhkov, Austin Buchanan, Sergiy Butenko, Vladimir Boginski

    The celebrated Motzkin–Straus formulation for the maximum clique problem provides a nontrivial characterization of the clique number of a graph in terms of the maximum value of a nonconvex quadratic function over a standard simplex. It was originally developed as a way of proving Turán’s theorem in graph theory, but was later used to develop competitive algorithms for the maximum clique problem based

    更新日期:2020-10-17
  • Sparse PSD approximation of the PSD cone
    Math. Program. (IF 2.823) Pub Date : 2020-10-16
    Grigoriy Blekherman, Santanu S. Dey, Marco Molinaro, Shengding Sun

    While semidefinite programming (SDP) problems are polynomially solvable in theory, it is often difficult to solve large SDP instances in practice. One technique to address this issue is to relax the global positive-semidefiniteness (PSD) constraint and only enforce PSD-ness on smaller \(k\times k\) principal submatrices—we call this the sparse SDP relaxation. Surprisingly, it has been observed empirically

    更新日期:2020-10-17
  • The generalized trust region subproblem: solution complexity and convex hull results
    Math. Program. (IF 2.823) Pub Date : 2020-10-10
    Alex L. Wang, Fatma Kılınç-Karzan

    We consider the generalized trust region subproblem (GTRS) of minimizing a nonconvex quadratic objective over a nonconvex quadratic constraint. A lifting of this problem recasts the GTRS as minimizing a linear objective subject to two nonconvex quadratic constraints. Our first main contribution is structural: we give an explicit description of the convex hull of this nonconvex set in terms of the generalized

    更新日期:2020-10-11
  • Error bounds for inequality systems defining convex sets
    Math. Program. (IF 2.823) Pub Date : 2020-10-06
    Joydeep Dutta, Juan Enrique Martínez-Legaz

    The main goal in this paper is to devise an approach to explicitly calculate the constant in the Hoffman’s error bound for (not necessarily convex) inequality systems defining convex sets. We give a constructive proof of the Hoffman’s error bound and show that we can use our method to calculate the constant at least in simple cases.

    更新日期:2020-10-07
  • A stability result for linear Markovian stochastic optimization problems
    Math. Program. (IF 2.823) Pub Date : 2020-10-06
    Adriana Kiszka, David Wozabal

    In this paper, we propose a semi-metric for Markov processes that allows to bound optimal values of linear Markovian stochastic optimization problems. Similar to existing notions of distance for general stochastic processes, our distance is based on transportation metrics. As opposed to the extant literature, the proposed distance is problem specific, i.e., dependent on the data of the problem whose

    更新日期:2020-10-07
  • An optimal monotone contention resolution scheme for bipartite matchings via a polyhedral viewpoint
    Math. Program. (IF 2.823) Pub Date : 2020-10-01
    Simon Bruggmann, Rico Zenklusen

    Relaxation and rounding approaches became a standard and extremely versatile tool for constrained submodular function maximization. One of the most common rounding techniques in this context are contention resolution schemes. Such schemes round a fractional point by first rounding each coordinate independently, and then dropping some elements to reach a feasible set. Also the second step, where elements

    更新日期:2020-10-02
  • Optimal sampled-data controls with running inequality state constraints: Pontryagin maximum principle and bouncing trajectory phenomenon
    Math. Program. (IF 2.823) Pub Date : 2020-10-01
    Loïc Bourdin, Gaurav Dhar

    In the present paper we derive a Pontryagin maximum principle for general nonlinear optimal sampled-data control problems in the presence of running inequality state constraints. We obtain, in particular, a nonpositive averaged Hamiltonian gradient condition associated with an adjoint vector being a function of bounded variation. As a well known challenge, theoretical and numerical difficulties may

    更新日期:2020-10-02
  • Projective splitting with forward steps
    Math. Program. (IF 2.823) Pub Date : 2020-09-30
    Patrick R. Johnstone, Jonathan Eckstein

    This work is concerned with the classical problem of finding a zero of a sum of maximal monotone operators. For the projective splitting framework recently proposed by Combettes and Eckstein, we show how to replace the fundamental subproblem calculation using a backward step with one based on two forward steps. The resulting algorithms have the same kind of coordination procedure and can be implemented

    更新日期:2020-10-02
  • Performance guarantees of local search for minsum scheduling problems
    Math. Program. (IF 2.823) Pub Date : 2020-09-30
    José R. Correa, Felipe T. Muñoz

    We study the worst-case performance guarantee of locally optimal solutions for the problem of minimizing the total weighted and unweighted completion time on parallel machine environments. Our method makes use of a mapping that maps a schedule into an inner product space so that the norm of the mapping is closely related to the cost of the schedule. We apply the method to study the most basic local

    更新日期:2020-10-02
  • 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
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