18 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…
Manuel Fischer, Akshay Gupte
We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player noncooperative games. We compare the formulations to common algorithms in Gambit, and conclude that a multilinear feasibility program finds a Nash equilibrium faster than any of the methods we compare it to…
Prerona Chatterjee, Deepanshu Kush, Shubhangi Saraf, Amir Shpilka
In this paper, we prove super-polynomial lower bounds for the model of sum of ordered set-multilinear algebraic branching programs, each with a possibly different ordering (PsmABP). Specifically, we give an explicit nd-variate polynomial of degree d such that any PsmABP computing it must have size n ω(1) for d as low…
Pacheco, Bruno Machado, Antunes, Pedro Marcolin + 10 more
This paper introduces a novel algorithm for Mixed-Integer Nonlinear Programming (MINLP) problems with multilinear interpolations of look-up tables. These problems arise when objectives or constraints contain black-box functions only known at a finite set of evaluations on a predefined grid. We derive a piecewise-linear…
Apolline J. R. Petit, Jeremy Guez, Arnaud Le Rouzic
The evolution of gene expression is constrained by the topology of gene regulatory networks, as co-expressed genes are likely to be affected together by mutations. Conversely, co-expression can also be an advantage when genes are under joint selection. Here, we assessed theoretically whether correlated selection…
Xuan Lin
This paper presents a comparative study of data-driven acceleration techniques for mixed-integer bilinear programs (MIBLPs) applied to robot motion planning. MIBLPs combine discrete decision variables and nonlinear constraints, making them computationally challenging for real-time robotics applications. We investigate…
Jean-Pierre Borg, Jacques Colinge, Patrice Ravel
Modular response analysis (MRA) is a well-established method to infer biological networks from perturbation data. Classically, MRA requires the solution of a linear system and results are sensitive to noise in the data and perturbation intensities. Applications to networks of 10 nodes or more are difficult due to noise…
Kenneth W. Latimer, David J. Freedman
Neurons in parietal cortex exhibit task-related activity during decision-making tasks. However, it remains unclear how long-term training to perform different tasks over months or even years shapes neural computations and representations. We examine lateral intraparietal area (LIP) responses during a visual motion…
Elisabeth Gaar, Jon Lee, Ivana Ljubić, Markus Sinnl + 1 more
We study a class of integer bilevel programs with second-order cone constraints at the upper-level and a convex-quadratic objective function and linear constraints at the lower-level. We develop disjunctive cuts (DCs) to separate bilevel-infeasible solutions using a second-order-cone-based cut-generating procedure. We…
Jean-Pierre Borg, Jacques Colinge, Patrice Ravel
Modular Response Analysis (MRA) is an effective method to infer biological networks from perturbation data. However, it has several limitations, such as strong sensitivity to noise, need of performing independent perturbations that hit a single node at a time, and linear approximation of dependencies within the…
Ahmad Abdi, Gérard Cornuéjols, Bertrand Guenin, Levent Tunçel
A rational number is dyadic if it has a finite binary representation $p/2^k$, where p is an integer and k is a nonnegative integer. Dyadic rationals are important for numerical computations because they have an exact representation in floating-point arithmetic on a computer. A vector is dyadic if all its entries are…
Parth Brahmbhatt, David L. Cole, Victor M. Zavala, Styliani Avraamidou
Using Graph Modeling and Multi-Parametric Programming Authors: Parth Brahmbhatt, David L. Cole, Victor M. Zavala, Styliani Avraamidou Benders decomposition is a widely used method for solving large and structured optimization problems, but its performance is affected by the repeated solution of subproblems. We propose…
Jing He, Qi-wei Kong, Ho-Chung Lui, Haitao Liu + 1 more
The definition of factor space and a unified optimization based classification model were developed for linear programming and supervised learning. Intelligent behaviour appeared in a decision process can be treated as a moving point y, the dynamic state observed and controlled by the agent, moving in a factor space…
Jiaqi Zheng, Antonios Varvitsiotis, Tiow-Seng Tan, Wayne Lin
In this paper, we introduce a primal-dual algorithmic framework for solving Symmetric Cone Programs (SCPs), a versatile optimization model that unifies and extends Linear, Second-Order Cone (SOCP), and Semidefinite Programming (SDP). Our work generalizes the primal-dual framework for SDPs introduced by Arora and Kale…
Pei Liu, Xiao Liang, Yue Li, Jiawei Luo
Systematic investigation of high-order molecular interactions can deepen our understanding of the mechanisms underlying biological systems. However, effectively capturing both multilinear and nonlinear relationships to accurately identify the complex triplet relationships remains a challenge. In this paper, we present…
Hao Hu, Renata Sotirov, Henry Wolkowicz
We consider both facial reduction, FR, and symmetry reduction, SR, techniques for semidefinite programming, SDP. We show that the two together fit surprisingly well in an alternating direction method of multipliers, ADMM, approach. In fact, this approach allows for simply adding on nonnegativity constraints, and…
Authors not listed
Experimental design plays an important role in efficiently acquiring informative data for system characterization and deriving robust conclusions under resource limitations. Recent advancements in high-throughput experimentation coupled with machine learning have notably improved experimental procedures. While Bayesian…
Mihailo Stojnic
polyhedrons Authors: ['Mihailo Stojnic'] We consider random linear programs (rlps) as a subclass of random optimization problems (rops) and study their typical behavior. Our particular focus is on appropriate linear objectives which connect the rlps to the mean widths of random polyhedrons/polytopes. Utilizing the…