21 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…
Kai Kellner
Disjointly constrained multilinear programming concerns the problem of maximizing a multilinear function on the product of finitely many disjoint polyhedra. While maximizing a linear function on a polytope (linear programming) is known to be solvable in polynomial time, even bilinear programming is NP-hard. Based on a…
Bahman Kalantari
On the one hand we state Nash equilibrium (NE) as a formal theorem on multilinear forms and give a pedagogically simple proof, free of game theory terminology. On the other hand, inspired by this formalism, we prove a multilinear minimax theorem, a generalization of von Neumann's bilinear minimax theorem. Next, we…
V. Arvind, S. Raja
In this paper, we study the structure of set-multilinear arithmetic circuits and set-multilinear branching programs with the aim of showing lower bound results. We define some natural restrictions of these models for which we are able to show lower bound results. Some of our results extend existing lower bounds, while…
Lei Wang, Min Fang
In this paper, we consider the multiobjective linear programs where coefficients in the objective function belong to uncertainty sets. We introduce the concept of robust efficient solutions to uncertain multiobjective linear programming problems. By using two scalarization methods, the weighted sum method and the…
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…
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…
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…
Matúš Benko, Helmut Gfrerer
In this paper, we consider a sufficiently broad class of non-linear mathematical programs with disjunctive constraints, which, e.g. include mathematical programs with complemetarity/vanishing constraints. We present an extension of the concept of Q-stationarity which can be easily combined with the well-known notion of…
Wei Wei
| A | | Basics of Linear and Conic Programs | 7 | | --- | --- | --- | --- | | | A.1 | Basic Notations 8 | | | | | A.1.1 Convex Sets 8 | | | | | A.1.2 Generalized Inequalities 13 | | | | | A.1.3 Dual Cones and Dual Generalized Inequalities 14 | | | | | A.1.4 Convex Function and Epigraph 16 | | | | A.2 | From Linear to…
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…
Bertha Vázquez-Rodríguez, Laura E. Suárez, Golia Shafiei, Ross D. Markello + 6 more
The white matter architecture of brain networks imparts a distinct signature on neuronal co-activation patterns. Inter-regional projections promote synchrony among distant neuronal populations, giving rise to richly patterned functional networks. A variety of statistical, communication and biophysical models have been…
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…
Oskar Weser, Björn Hein Hanke, Ricardo Mata
In this work, we present a fully automated method for the construction of chemically meaningful sets of non-redundant internal coordinates (also commonly denoted as Z-matrices) from the cartesian coordinates of a molecular system. Particular focus is placed on avoiding ill-definitions of angles and dihedrals due to…
J. Stoer
Infeasible-interior-point paths are the main tools in interior-point methods for solving many kinds of optimization problems. These paths are usually parametrized by a penalty-parameter r ↓ 0 and further parameters describing their off-centrality and infeasiblilty. Starting with an early result of C. Witzgall et al.…
Oliver Serang, Jérémie Bourdon
Linear programming (LP) problems are commonly used in analysis and resource allocation, frequently surfacing as approximations to more difficult problems. Existing approaches to LP have been dominated by a small group of methods, and randomized algorithms have not enjoyed popularity in practice. This paper introduces a…
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…
Riley Hickman, Priyansh Parakh, Austin Cheng, Qianxiang Ai + 3 more
Experiment planning algorithms are a required component of autonomous platforms for scientific discovery. Selecting a suitable optimization algorithm for a novel application is an important yet difficult choice a researcher has to make based on past empirical performance on similar tasks. To facilitate the evaluation…
Jógvan Magnus Haugaard Olsen, Viacheslav Bolnykh, Simone Meloni, Emiliano Ippoliti + 3 more
We present a flexible and efficient framework for multiscale modeling in computational chemistry (MiMiC). It is based on a multiple-program multiple-data (MPMD) model with loosely coupled programs. Fast data exchange between programs is achieved through the use of MPI intercommunicators. This allows exploiting the…
Frederik Wieder, Martin Henk, Alexander Bockmayr
Elementary flux modes (EFMs) play an important role in metabolic network analysis. Here we study geometric properties of EFMs. In particular, we are interested in the distribution of EFMs in the face lattice of the steady-state flux cone of a metabolic network. The number of EFMs can be exponentially large in the…