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Search · four archives
25 papers · ranked by Valyu relevance
Abraham P. Punnen, Navpreet Kaur
optimization problem Authors: ['Abraham P. Punnen' 'Navpreet Kaur'] In this paper, we present several new linearizations of a quadratic binary optimization problem (QBOP), primarily using the method of aggregations. Although aggregations were studied in the past in the context of solving system of Diophantine equations…
Esma Yildirim
We consider linear and semidefinite programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT relaxation), and the Shor relaxation combined with the RLT relaxation (SDP-RLT relaxation). By incorporating the firstorder optimality conditions, a quadratic program can…
Yingfeng Zhao, Sanyang Liu
We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique.…
Libor Barto, Silvia Butti
In a recent line of work, Butti and Dalmau have shown that a fixed-template Constraint Satisfaction Problem is solvable by a certain natural linear programming relaxation (equivalent to the basic linear programming relaxation) if and only if it is solvable on a certain distributed network, and this happens if and only…
Jorge Carrasco Muriel, Christopher Long, Nikolaus Sonnenschein
GEnome-scale Metabolic (GEM) models are knowledge bases of the reactions and metabolites of a particular organism. These GEM models allow for the simulation of the metabolism - e.g. calculating growth and production yields - based on the stoichiometry, reaction directionality and uptake rates of the metabolic network.…
Hao Cheng, Keyu Xu, Kuruvilla Joseph Abraham
Low-cost genome-wide single-nucleotide polymorphisms (SNPs) are routinely used in animal breeding programs. Compared to SNP arrays, the use of whole-genome sequence data generated by the next-generation sequencing technologies (NGS) has great potential in livestock populations. However, a large number of animals are…
Mohamed Amin Ben Sassi, Sriram Sankaranarayanan
In this paper, we examine linear programming (LP) relaxations based on Bernstein polynomials for polynomial optimization problems (POPs). We present a progression of increasingly more precise LP relaxations based on expressing the given polynomial in its Bernstein form, as a linear combination of Bernstein polynomials.…
Gennadiy Averkov, Matthias Schymura
For a set X of integer points in a polyhedron, the smallest number of facets of any polyhedron whose set of integer points coincides with X is called the relaxation complexity ${{\,\mathrm{rc}\,}}X$. This parameter, introduced by Kaibel & Weltge (2015), captures the complexity of linear descriptions of X without using…
Li Ge, Sanyang Liu
To globally solve a nonconvex quadratic programming problem, this paper presents an accelerating linearizing algorithm based on the framework of the branch-and-bound method. By utilizing a new linear relaxation approach, the initial quadratic programming problem is reduced to a sequence of linear relaxation programming…
Immanuel Bomze, Bo Peng, Yuzhou Qiu, E. Alper Yıldırım
Standard quadratic optimization problems (StQPs) provide a versatile modelling tool in various applications. In this paper, we consider StQPs with a hard sparsity constraint, referred to as sparse StQPs. We focus on various tractable convex relaxations of sparse StQPs arising from a mixed-binary quadratic formulation…
Sven Mallach
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients and right hand sides. Quadratic constraints may exist in addition, and the…
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…
Renichiro Haba, Masayuki Ohzeki, Kazuyuki Tanaka, Dennis Salahub
Quantum annealing has garnered significant attention as meta-heuristics inspired by quantum physics for combinatorial optimization problems. Among its many applications, nonnegative/binary matrix factorization stands out for its complexity and relevance in unsupervised machine learning. The use of reverse annealing, a…
Hendrik Schawe, Roman Bleim, Alexander K. Hartmann, Andrea Gambassi
Here we study linear programming applied to the random K-SAT problem, a fundamental problem in computational complexity. The K-SAT problem is to decide whether a Boolean formula with N variables and structured as a conjunction of M clauses, each being a disjunction of K variables or their negations is satisfiable or…
Hao Hu, Boshi Yang
Relaxations of Combinatorial Problems Authors: ['Hao Hu' 'Boshi Yang'] We develop a new method called affine FR for recovering Slater's condition for semidefinite programming (SDP) relaxations of combinatorial optimization (CO) problems. Affine FR is a user-friendly method, as it is fully automatic and only requires a…
Henri Schmidt, Benjamin J. Raphael
Reconstructing unobserved ancestral states of a phylogenetic tree provides insight into the history of evolving systems and is one of the fundamental problems in phylogenetics. For a fixed phylogenetic tree, the most parsimonious ancestral reconstruction – a solution to the small parsimony problem – can be efficiently…
Mark A. Hallen
Protein design algorithms must search an enormous conformational space to identify favorable conformations. As a result, those that perform this search with guarantees of accuracy generally start with a conformational pruning step, such as dead-end elimination (DEE). However, the mathematical assumptions of DEE-based…
Deepak Ponvel Chermakani
- We present a polynomial-time algorithm that obtains a set of Asymptotic Linear Programs (ALPs) from a given linear system S, such that one of these ALPs admits a feasible solution if and only if S admits a feasible solution. We also show how to use the same algorithm to determine whether or not S admits a non-trivial…
Chuan-Hao Guo, Yuan Guo, Bei-Bei Liu
The densest k-subgraph (DkS) maximization problem is to find a set of k vertices with maximum total weight of edges in the subgraph induced by this set. This problem is in general NP-hard. In this paper, two relaxation methods for solving the DkS problem are presented. One is doubly nonnegative relaxation, and the…
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…
Qianxiang Ai, Joshua Schrier
In a recent paper in this journal (Chem. Mater. 2022, 34, 2545-2552), Twyman et al. studied the environmental stability of crystals by introducing a greedy heuristic algorithm for determining possible oxidation reactions. We show how the problem can be solved exactly, with less code and comparable computational time by…
Or Zuk
We define and study the problem of genomic block selection for multiple complex traits. In this problem, one constructs a genome by selecting different genomic parts (e.g. chromosomes) from different source genomes. The constructed genome is associated with a vector of polygenic scores, obtained by summing the…
Sungho Shin, Ophelia Venturelli, Victor M. Zavala
We present a nonlinear programming (NLP) framework for the scalable solution of parameter estimation problems that arise in dynamic modeling of biological systems. Such problems are computationally challenging because they often involve highly nonlinear and stif differential equations as well as many experimental data…
Authors not listed
Automated chemistry platforms hold the potential to enable large-scale organic synthesis campaigns, such as producing a library of compounds for biological evaluation. The efficiency of such platforms will depend on the schedule according to which the synthesis operations are executed. In this work, we study the…
Daniel Machado
Genome-scale metabolic modeling is a powerful framework for predicting metabolic phenotypes of any organism with an annotated genome. For two decades, this framework has been used for rational design of microbial cell factories. In the last decade, the range of applications has exploded, and new frontiers have emerged…