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Search · four archives
11 papers · ranked by Valyu relevance
Arvind U. Raghunathan, Carlos Cardonha, David J. Bergman, Carlos Nohra
'Carlos Nohra'] Linear programming (LP) relaxations are widely employed in exact solution methods for multilinear programs (MLP). One example is the family of Recursive McCormick Linearization (RML) strategies, where bilinear products are substituted for artificial variables, which deliver a relaxation of the original…
Emily Schutte, Matthias Walter
We consider linear relaxations for multilinear optimization problems. In a recent paper, Khajavirad proved that the extended flower relaxation is at least as strong as the relaxation of any recursive McCormick linearization (Operations Research Letters 51 (2023) 146–152). In this paper we extend the result to more…
Aida Khajavirad
Recursive McCormick relaxations are among the most popular convexification techniques for binary polynomial optimization. It is well-understood that both the quality and the size of these relaxations depend on the recursive sequence and finding an optimal sequence amounts to solving a difficult combinatorial…
Oleg Stepanov, Alexey Isaev, Elena Dranitsyna, Yulia Litvinenko
A class of nonlinear filtering problems connected with data fusion from various navigation sensors and a navigation system is considered. A special feature of these problems is that the posterior probability density function (PDF) of the state vector being estimated changes its character from multi-extremal to…
Mikołaj Myszkowski
Recurrence relations arise in various fields of mathematics and prove to be a powerful tool for studying probability [1] and combinatorics [2]. It is often the case that construction of a solution to a mathematical problem simplifies to solving a recurrence relation. The theory of linear recurrences is well studied…
Peter L. Bartlett, Chris Junchi Li, Jingfeng Wu, Bin Yu
In the field of optimization, developing accelerated methods for solving minimax and fixed-point problems remains a fundamental challenge. This paper presents a novel family of dual accelerated algorithms that achieve optimal convergence rates for both minimax and fixed-point problems. By exploring new anchoring…
Eranda Çela, Bettina Klinz, Stefan Lendl, Gerhard J. Woeginger + 1 more
'Lasse Wulf'] An instance of the NP-hard Quadratic Shortest Path Problem (QSPP) is called linearizable iff it is equivalent to an instance of the classic Shortest Path Problem (SPP) on the same input digraph. The linearization problem for the QSPP (LinQSPP) decides whether a given QSPP instance is linearizable and…
Luis Verde‐Star
A sequence of polynomials {pn(t)}n≥0 in one real or complex variable such that pn has degree n, for n ≥ 0, is called a polynomial sequence and it is a basis for the algebra of all polynomials in t. Therefore every polynomial ur(t) of degree r has a unique representation of the form
George Haller, Bálint Kaszás
Dynamic mode decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly in others, a clarification of the assumptions under which DMD is applicable is…
Yiteng Zhang, Zixiong Wang, Xingyu Li, Bin Min
Inferring computational mechanisms from neural recordings is a central goal in systems neuro-science. Recent developments have identified low-rank recurrent neural networks (RNNs) as an effective tool for fitting observed neural activity and extracting neural dynamics. However, we show that accurate activity fitting…
Sangyeon Lee, Hanjin Kim, Doheon Lee
Regression analysis is one of the most widely applied methods in many fields including bio-medical study. Dimensionality reduction is also widely used for data preprocessing and feature selection analysis, to extract high-impact features from the predictions. As the complexity of both data and prediction models…