
Separating Variables in Bivariate Polynomial Ideals
We present an algorithm which for any given ideal Iāš [x,y] finds all el...
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Fair Sparse Regression with Clustering: An Invex Relaxation for a Combinatorial Problem
In this paper, we study the problem of fair sparse regression on a biase...
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Nfold integer programming via LP rounding
We consider Nfold integer programming problems. After a decade of conti...
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Combinatorial Optimization with PhysicsInspired Graph Neural Networks
We demonstrate how graph neural networks can be used to solve combinator...
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Compressed Quadratization of Higher Order Binary Optimization Problems
Recent hardware advances in quantum and quantuminspired annealers promi...
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Quantum Algorithms for Optimization and Polynomial Systems Solving over Finite Fields
In this paper, we give quantum algorithms for two fundamental computatio...
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Higher Order Maximum Persistency and Comparison Theorems
We address combinatorial problems that can be formulated as minimization...
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Integrality of Linearizations of Polynomials over Binary Variables using Additional Monomials
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an integral relaxation polytope, generalizing work by Del Pia and Khajavirad (SIAM Journal on Optimization, 2018). We also present an algorithm that finds these extra monomials for a given polynomial to yield an integral relaxation polytope or determines that no such set of extra monomials exists. In the former case, our approach yields an algorithm to solve the given polynomial optimization problem as a compact LP, and we complement this with a purely combinatorial algorithm.
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