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Sum-of-squares relaxations for polynomial min–max problems over simple sets Math. Program. (IF 2.7) Pub Date : 2024-03-15
Abstract We consider min–max optimization problems for polynomial functions, where a multivariate polynomial is maximized with respect to a subset of variables, and the resulting maximal value is minimized with respect to the remaining variables. When the variables belong to simple sets (e.g., a hypercube, the Euclidean hypersphere, or a ball), we derive a sum-of-squares formulation based on a primal-dual
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A slightly lifted convex relaxation for nonconvex quadratic programming with ball constraints Math. Program. (IF 2.7) Pub Date : 2024-03-14 Samuel Burer
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Perseus: a simple and optimal high-order method for variational inequalities Math. Program. (IF 2.7) Pub Date : 2024-03-13 Tianyi Lin, Michael I. Jordan
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Generalized Nash equilibrium problems with mixed-integer variables Math. Program. (IF 2.7) Pub Date : 2024-03-13
Abstract We consider generalized Nash equilibrium problems (GNEPs) with non-convex strategy spaces and non-convex cost functions. This general class of games includes the important case of games with mixed-integer variables for which only a few results are known in the literature. We present a new approach to characterize equilibria via a convexification technique using the Nikaido–Isoda function.
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The Chvátal–Gomory procedure for integer SDPs with applications in combinatorial optimization Math. Program. (IF 2.7) Pub Date : 2024-03-13
Abstract In this paper we study the well-known Chvátal–Gomory (CG) procedure for the class of integer semidefinite programs (ISDPs). We prove several results regarding the hierarchy of relaxations obtained by iterating this procedure. We also study different formulations of the elementary closure of spectrahedra. A polyhedral description of the elementary closure for a specific type of spectrahedra
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Generalized minimum 0-extension problem and discrete convexity Math. Program. (IF 2.7) Pub Date : 2024-03-07 Martin Dvorak, Vladimir Kolmogorov
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Matroid-based TSP rounding for half-integral solutions Math. Program. (IF 2.7) Pub Date : 2024-03-06
Abstract We show how to round any half-integral solution to the subtour-elimination relaxation for the TSP, while losing a less-than \(-\) 1.5 factor. Such a rounding algorithm was recently given by Karlin, Klein, and Oveis Gharan based on sampling from max-entropy distributions. We build on an approach of Haddadan and Newman to show how sampling from the matroid intersection polytope, combined with
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On convergence of iterative thresholding algorithms to approximate sparse solution for composite nonconvex optimization Math. Program. (IF 2.7) Pub Date : 2024-03-06 Yaohua Hu, Xinlin Hu, Xiaoqi Yang
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Polyhedral properties of RLT relaxations of nonconvex quadratic programs and their implications on exact relaxations Math. Program. (IF 2.7) Pub Date : 2024-03-06 Yuzhou Qiu, E. Alper Yıldırım
We study linear programming relaxations of nonconvex quadratic programs given by the reformulation–linearization technique (RLT), referred to as RLT relaxations. We investigate the relations between the polyhedral properties of the feasible regions of a quadratic program and its RLT relaxation. We establish various connections between recession directions, boundedness, and vertices of the two feasible
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Multiplicative auction algorithm for approximate maximum weight bipartite matching Math. Program. (IF 2.7) Pub Date : 2024-03-06
Abstract We present an auction algorithm using multiplicative instead of constant weight updates to compute a \((1-\varepsilon )\) -approximate maximum weight matching (MWM) in a bipartite graph with n vertices and m edges in time \(O(m\varepsilon ^{-1})\) , beating the running time of the fastest known approximation algorithm of Duan and Pettie [JACM ’14] that runs in \(O(m\varepsilon ^{-1}\log \varepsilon
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Level constrained first order methods for function constrained optimization Math. Program. (IF 2.7) Pub Date : 2024-03-06 Digvijay Boob, Qi Deng, Guanghui Lan
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Hessian barrier algorithms for non-convex conic optimization Math. Program. (IF 2.7) Pub Date : 2024-03-04 Pavel Dvurechensky, Mathias Staudigl
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The effect of smooth parametrizations on nonconvex optimization landscapes Math. Program. (IF 2.7) Pub Date : 2024-03-04 Eitan Levin, Joe Kileel, Nicolas Boumal
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Semiglobal exponential stability of the discrete-time Arrow-Hurwicz-Uzawa primal-dual algorithm for constrained optimization Math. Program. (IF 2.7) Pub Date : 2024-02-12 Michelangelo Bin, Ivano Notarnicola, Thomas Parisini
We consider the discrete-time Arrow-Hurwicz-Uzawa primal-dual algorithm, also known as the first-order Lagrangian method, for constrained optimization problems involving a smooth strongly convex cost and smooth convex constraints. We prove that, for every given compact set of initial conditions, there always exists a sufficiently small stepsize guaranteeing exponential stability of the optimal primal-dual
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A general framework for multi-marginal optimal transport Math. Program. (IF 2.7) Pub Date : 2024-02-05 Brendan Pass, Adolfo Vargas-Jiménez
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Frank–Wolfe-type methods for a class of nonconvex inequality-constrained problems Math. Program. (IF 2.7) Pub Date : 2024-02-03
Abstract The Frank–Wolfe (FW) method, which implements efficient linear oracles that minimize linear approximations of the objective function over a fixed compact convex set, has recently received much attention in the optimization and machine learning literature. In this paper, we propose a new FW-type method for minimizing a smooth function over a compact set defined as the level set of a single
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Designing tractable piecewise affine policies for multi-stage adjustable robust optimization Math. Program. (IF 2.7) Pub Date : 2024-02-03 Simon Thomä, Grit Walther, Maximilian Schiffer
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A constant-factor approximation for generalized malleable scheduling under $$M ^{\natural }$$ -concave processing speeds Math. Program. (IF 2.7) Pub Date : 2024-01-29 Dimitris Fotakis, Jannik Matuschke, Orestis Papadigenopoulos
In generalized malleable scheduling, jobs can be allocated and processed simultaneously on multiple machines so as to reduce the overall makespan of the schedule. The required processing time for each job is determined by the joint processing speed of the allocated machines. We study the case that processing speeds are job-dependent \(M ^{\natural }\)-concave functions and provide a constant-factor
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Adjustability in robust linear optimization Math. Program. (IF 2.7) Pub Date : 2024-01-27
Abstract We investigate the concept of adjustability—the difference in objective values between two types of dynamic robust optimization formulations: one where (static) decisions are made before uncertainty realization, and one where uncertainty is resolved before (adjustable) decisions. This difference reflects the value of information and decision timing in optimization under uncertainty, and is
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Characterization of matrices with bounded Graver bases and depth parameters and applications to integer programming Math. Program. (IF 2.7) Pub Date : 2024-01-20 Marcin Briański, Martin Koutecký, Daniel Král’, Kristýna Pekárková, Felix Schröder
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Constrained optimization of rank-one functions with indicator variables Math. Program. (IF 2.7) Pub Date : 2024-01-20 Soroosh Shafiee, Fatma Kılınç-Karzan
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A competitive algorithm for throughput maximization on identical machines Math. Program. (IF 2.7) Pub Date : 2024-01-10 Benjamin Moseley, Kirk Pruhs, Clifford Stein, Rudy Zhou
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Counterexample and an additional revealing poll step for a result of “analysis of direct searches for discontinuous functions” Math. Program. (IF 2.7) Pub Date : 2024-01-08
Abstract This note provides a counterexample to a theorem announced in the last part of the paper (Vicente and Custódio Math Program 133:299–325, 2012). The counterexample involves an objective function \(f: \mathbb {R}\rightarrow \mathbb {R}\) which satisfies all the assumptions required by the theorem but contradicts some of its conclusions. A corollary of this theorem is also affected by this counterexample
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No dimension-free deterministic algorithm computes approximate stationarities of Lipschitzians Math. Program. (IF 2.7) Pub Date : 2024-01-06 Lai Tian, Anthony Man-Cho So
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Complementary composite minimization, small gradients in general norms, and applications Math. Program. (IF 2.7) Pub Date : 2024-01-05 Jelena Diakonikolas, Cristóbal Guzmán
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We introduce a new algorithmic framework for complementary composite minimization, where the objective function decouples into a (weakly) smooth and a uniformly convex term
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High-order methods beyond the classical complexity bounds: inexact high-order proximal-point methods Math. Program. (IF 2.7) Pub Date : 2024-01-04 Masoud Ahookhosh, Yurii Nesterov
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FPT algorithms for a special block-structured integer program with applications in scheduling Math. Program. (IF 2.7) Pub Date : 2024-01-04
Abstract In this paper, a special case of the generalized 4-block n-fold IPs is investigated, where \(B_i=B\) and B has a rank at most 1. Such IPs, called almost combinatorial 4-block n-fold IPs, include the generalized n-fold IPs as a subcase. We are interested in fixed parameter tractable (FPT) algorithms by taking as parameters the dimensions of the blocks and the largest coefficient. For almost
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A 2-approximation for the bounded treewidth sparsest cut problem in $$\textsf{FPT}$$ Time Math. Program. (IF 2.7) Pub Date : 2024-01-04 Vincent Cohen-Addad, Tobias Mömke, Victor Verdugo
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Asymmetry in the complexity of the multi-commodity network pricing problem Math. Program. (IF 2.7) Pub Date : 2024-01-03 Quang Minh Bui, Margarida Carvalho, José Neto
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The exact worst-case convergence rate of the alternating direction method of multipliers Math. Program. (IF 2.7) Pub Date : 2023-12-26 Moslem Zamani, Hadi Abbaszadehpeivasti, Etienne de Klerk
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First order asymptotics of the sample average approximation method to solve risk averse stochastic programs Math. Program. (IF 2.7) Pub Date : 2023-12-26 Volker Krätschmer
We investigate statistical properties of the optimal value of the Sample Average Approximation of stochastic programs, continuing the study (Krätschmer in Nonasymptotic upper estimates for errors of the sample average approximation method to solve risk averse stochastic programs, 2023. Forthcoming in SIAM J. Optim.). Central Limit Theorem type results are derived for the optimal value. As a crucial
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Beyond symmetry: best submatrix selection for the sparse truncated SVD Math. Program. (IF 2.7) Pub Date : 2023-12-21
Abstract The truncated singular value decomposition (SVD), also known as the best low-rank matrix approximation with minimum error measured by a unitarily invariant norm, has been applied to many domains such as biology, healthcare, among others, where high-dimensional datasets are prevalent. To extract interpretable information from the high-dimensional data, sparse truncated SVD (SSVD) has been used
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Intersecting and dense restrictions of clutters in polynomial time Math. Program. (IF 2.7) Pub Date : 2023-12-18 Martin Drees
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Hardness and approximation of submodular minimum linear ordering problems Math. Program. (IF 2.7) Pub Date : 2023-12-14 Majid Farhadi, Swati Gupta, Shengding Sun, Prasad Tetali, Michael C. Wigal
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A single cut proximal bundle method for stochastic convex composite optimization Math. Program. (IF 2.7) Pub Date : 2023-12-11 Jiaming Liang, Vincent Guigues, Renato D. C. Monteiro
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Quasi-polynomial time approximation schemes for assortment optimization under Mallows-based rankings Math. Program. (IF 2.7) Pub Date : 2023-12-11 Alon Rieger, Danny Segev
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Efficient Kirszbraun extension with applications to regression Math. Program. (IF 2.7) Pub Date : 2023-12-07 Hananel Zaichyk, Armin Biess, Aryeh Kontorovich, Yury Makarychev
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A polynomial time algorithm for finding a minimum 4-partition of a submodular function Math. Program. (IF 2.7) Pub Date : 2023-12-06 Tsuyoshi Hirayama, Yuhao Liu, Kazuhisa Makino, Ke Shi, Chao Xu
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New lower bounds on crossing numbers of $$K_{m,n}$$ from semidefinite programming Math. Program. (IF 2.7) Pub Date : 2023-11-20 Daniel Brosch, Sven C. Polak
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State polynomials: positivity, optimization and nonlinear Bell inequalities Math. Program. (IF 2.7) Pub Date : 2023-11-03 Igor Klep, Victor Magron, Jurij Volčič, Jie Wang
This paper introduces state polynomials, i.e., polynomials in noncommuting variables and formal states of their products. A state analog of Artin’s solution to Hilbert’s 17th problem is proved showing that state polynomials, positive over all matrices and matricial states, are sums of squares with denominators. Somewhat surprisingly, it is also established that a Krivine–Stengle Positivstellensatz
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Scalable adaptive cubic regularization methods Math. Program. (IF 2.7) Pub Date : 2023-10-31 Jean-Pierre Dussault, Tangi Migot, Dominique Orban
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The limits of local search for weighted k-set packing Math. Program. (IF 2.7) Pub Date : 2023-10-28 Meike Neuwohner
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Optimal item pricing in online combinatorial auctions Math. Program. (IF 2.7) Pub Date : 2023-10-28 José Correa, Andrés Cristi, Andrés Fielbaum, Tristan Pollner, S. Matthew Weinberg
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Inapproximability of shortest paths on perfect matching polytopes Math. Program. (IF 2.7) Pub Date : 2023-10-21 Jean Cardinal, Raphael Steiner
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Global optimization for cardinality-constrained minimum sum-of-squares clustering via semidefinite programming Math. Program. (IF 2.7) Pub Date : 2023-10-12 Veronica Piccialli, Antonio M. Sudoso
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Relaxations and duality for multiobjective integer programming Math. Program. (IF 2.7) Pub Date : 2023-10-12 Alex Dunbar, Saumya Sinha, Andrew J. Schaefer
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Global stability of first-order methods for coercive tame functions Math. Program. (IF 2.7) Pub Date : 2023-10-06 Cédric Josz, Lexiao Lai
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The density of planar sets avoiding unit distances Math. Program. (IF 2.7) Pub Date : 2023-10-06 Gergely Ambrus, Adrián Csiszárik, Máté Matolcsi, Dániel Varga, Pál Zsámboki
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Multiplicative updates for symmetric-cone factorizations Math. Program. (IF 2.7) Pub Date : 2023-09-30 Yong Sheng Soh, Antonios Varvitsiotis
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Better-than- $$\frac{4}{3}$$ -approximations for leaf-to-leaf tree and connectivity augmentation Math. Program. (IF 2.7) Pub Date : 2023-09-26 Federica Cecchetto, Vera Traub, Rico Zenklusen
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Residuals-based distributionally robust optimization with covariate information Math. Program. (IF 2.7) Pub Date : 2023-09-26 Rohit Kannan, Güzin Bayraksan, James R. Luedtke
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Sparse multi-term disjunctive cuts for the epigraph of a function of binary variables Math. Program. (IF 2.7) Pub Date : 2023-09-21 Rui Chen, James Luedtke
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Homotopic policy mirror descent: policy convergence, algorithmic regularization, and improved sample complexity Math. Program. (IF 2.7) Pub Date : 2023-09-19 Yan Li, Guanghui Lan, Tuo Zhao
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Neural networks with linear threshold activations: structure and algorithms Math. Program. (IF 2.7) Pub Date : 2023-09-12 Sammy Khalife, Hongyu Cheng, Amitabh Basu
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Deterministic enumeration of all minimum cut-sets and k-cut-sets in hypergraphs for fixed k Math. Program. (IF 2.7) Pub Date : 2023-09-12 Calvin Beideman, Karthekeyan Chandrasekaran, Weihang Wang
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Stochastic algorithms with geometric step decay converge linearly on sharp functions Math. Program. (IF 2.7) Pub Date : 2023-09-05 Damek Davis, Dmitriy Drusvyatskiy, Vasileios Charisopoulos
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A polynomial-size extended formulation for the multilinear polytope of beta-acyclic hypergraphs Math. Program. (IF 2.7) Pub Date : 2023-08-28 Alberto Del Pia, Aida Khajavirad
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New characterizations of strategy-proofness under single-peakedness Math. Program. (IF 2.7) Pub Date : 2023-08-28 Andrew B. Jennings, Rida Laraki, Clemens Puppe, Estelle M. Varloot
We provide novel representations of strategy-proof voting rules applicable when voters have uni-dimensional single-peaked preferences. In particular, we introduce a ‘grading curve’ representation which is particularly useful when introducing variable electorates. Our analysis recovers, links and unifies existing results in the literature, and provides new characterizations when strategy-proofness is
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A new complexity metric for nonconvex rank-one generalized matrix completion Math. Program. (IF 2.7) Pub Date : 2023-08-16 Haixiang Zhang, Baturalp Yalcin, Javad Lavaei, Somayeh Sojoudi
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The simultaneous semi-random model for TSP Math. Program. (IF 2.7) Pub Date : 2023-08-11 Eric Balkanski, Yuri Faenza, Mathieu Kubik