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作者：Diao, Shuotao; Sen, Suvrajeet
作者单位：Great Bay University; University of Southern California; University of Arizona; Birla Institute of Technology & Science Pilani (BITS Pilani)
摘要：Stochastic programming models can lead to very large-scale optimization problems for which it may be impossible to enumerate all possible scenarios. In such cases, one adopts a sampling-based solution methodology in which case the reliability of the resulting decisions may be suspect. For such instances, it is advisable to adopt methodologies that promote variance reduction. One such approach goes under a framework known as compromise decision, which requires multiple replications of the solut...
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作者：van Rossum, Bart; Chen, Rui; Lodi, Andrea
作者单位：Eindhoven University of Technology; The Chinese University of Hong Kong, Shenzhen
摘要：We consider range minimization problems featuring exponentially many variables, as frequently arising in fairness-oriented or bi-objective optimization. While branch and price is successful at solving cost-oriented problems with many variables, the performance of classical branch-and-price algorithms for range minimization is drastically impaired by weak linear programming relaxations. We propose range branching, a generic branching rule that directly tackles this issue and can be used on top ...
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作者：He, Ziyu; Liu, Junyi; Pang, Jong-Shi
作者单位：University of Southern California; University of Southern California; Tsinghua University
摘要：This paper explores Logarithmic Integral Optimization (LIO) problems, providing a unified computational framework for various tasks in computational statistics. Key among these are Maximum Likelihood Estimation (MLE) and Maximum a Posteriori (MAP) inference for probabilistic models. Specifically, we investigate scenarios where the model consists of conditional density functions with intractable normalizers. This feature can pose substantial computational challenges for the associated LIO, espe...
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作者：Lejeune, Miguel; Romeijnders, Ward; Krokhmal, Pavlo
作者单位：George Washington University; University of Groningen; University of Arizona
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作者：Carrasco, Pablo; Munoz, Gonzalo
作者单位：Universidad de Chile
摘要：The non-convex nature of trained neural networks has created significant obstacles in their incorporation into optimization models. In this context, Anderson et al. (2020) provided a framework to obtain the convex hull of the graph of a piecewise linear convex activation function composed with an affine function; this effectively convexifies activations such as the ReLU together with the affine transformation that precedes it. In this article, we contribute to this line of work by developing a...
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作者：Luo, Honglin; Wang, Xianfu; Wang, Ziyuan; Yang, Xinmin
作者单位：Chongqing Normal University
摘要：Level proximal subdifferential was introduced by Rockafellar recently for studyingproximal mappings of possibly nonconvex functions. In this paper a systematic studyof level proximal subdifferential is given. We characterize variational convexity of afunction by local firm nonexpansiveness of proximal mappings or local relative mono-tonicity of level proximal subdifferential, and use them to study local convergence ofproximal gradient method and others for variationally convex functions. Varia...
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作者：Chen, Renjie; Xu, Huifu; Zahle, Henryk
作者单位：Chinese University of Hong Kong; Saarland University
摘要：Finding an approximation of the inverse of the covariance matrix, also known as precision matrix, of a random vector with empirical data is widely discussed in finance and engineering. In data-driven problems, empirical data may be contaminated. This raises the question as to whether the approximate precision matrix is reliable from a statistical point of view. In this paper, we concentrate on a much-noticed sparse estimator of the precision matrix and investigate the issue from the perspectiv...
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作者：Carmon, Yair; Hinder, Oliver
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：We prove impossibility results for adaptivity in non-smooth stochastic convex optimization. Given a set of problem parameters we wish to adapt to, we define a price of adaptivity (PoA) that, roughly speaking, measures the multiplicative increase in suboptimality due to uncertainty in these parameters. When the initial distance to the optimum is unknown but a gradient norm bound is known, we show that the PoA is at least logarithmic for expected suboptimality, and double-logarithmic for median ...
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作者：Aragon-Artacho, Francisco J.; Perez-Aros, Pedro; Torregrosa-Belen, David
作者单位：Universitat d'Alacant; Universidad de Chile; Universidad de Chile
摘要：In this paper we introduce the Boosted Double-proximal Subgradient Algorithm (BDSA), a novel splitting algorithm designed to address general structured nonsmooth and nonconvex mathematical programs expressed as sums and differences of composite functions. BDSA exploits the combined nature of subgradients from the data and proximal steps, and integrates a linesearch procedure to enhance its performance. While BDSA encompasses existing schemes proposed in the literature, it extends its applicabi...
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作者：Hoppenot, Pierre; Martin, Mathis; Szigeti, Zoltan
作者单位：Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA)
