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Hyperbolic polynomials is a class of real-roots polynomials that has wide range of applications in theoretical computer science.
Maximization of a linear function of variables subject to linear inequalities
George B Dantzig · 1947
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Linear hyperbolic partial differential equations with constant coefficients
Lars Gårding · 1951
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Differential equations, difference equations and matrix theory
Peter D Lax · 1957
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An inequality for hyperbolic polynomials
Lars Gårding · 1959
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Polynomial algorithms in linear programming
Leonid G Khachiyan · 1980
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A new polynomial-time algorithm for linear programming
N. Karmarkar · 1984
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A polynomial-time algorithm, based on Newton’s method, for linear programming
James Renegar · 1988
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A new algorithm for minimizing convex functions over convex sets
Pravin M Vaidya · 1989
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Speeding-up linear programming using fast matrix multiplication
Pravin M Vaidya · 1989
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Linear programming, complexity theory and elementary functional analysis
James Renegar · 1995
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Hyperbolic polynomials and interior point methods for convex programming
Osman Güler · 1997
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Hyperbolic programs, and their derivative relaxations
James Renegar · 2004
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The lax conjecture is true
Adrian Lewis, Pablo Parrilo, and Motakuri Ramana · 2005
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Linear matrix inequality representation of sets
J William Helton and Victor Vinnikov · 2007
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Multivariate stable polynomials: theory and applications
David Wagner · 2011
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Hyperbolicity and stable polynomials in combinatorics and probability
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Lmi representations of convex semialgebraic sets and determinantal representations of algebraic hypersurfaces: past, present, and future
Victor Vinnikov · 2012
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Hyperbolicity cones of elementary symmetric polynomials are spectrahedral
Petter Brändén · 2014
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Path finding methods for linear programming: Solving linear programs in O ( r a n k ) {O}(\sqrt{rank}) iterations and faster algorithms for maximum flow
Yin Tat Lee and Aaron Sidford · 2014
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A polynomial-time affine-scaling method for semidefinite and hyperbolic programming
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A nearly-linear time algorithm for linear programs with small treewidth: A multiscale representation of robust central path
Sally Dong, Yin Tat Lee, and Guanghao Ye · 2021
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Minimizing convex functions with integral minimizers
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Faster dynamic matrix inverse for faster lps
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Fast sketching of polynomial kernels of polynomial degree
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Oblivious sketching-based central path method for solving linear programming problems
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Does preprocessing help training over-parameterized neural networks?
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Training multi-layer over-parametrized neural network in subquadratic time
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A faster small treewidth sdp solver
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Minimizing convex functions with rational minimizers
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Convex minimization with integral minima in O ~ ( n 4 ) \widetilde{O}(n^{4}) time
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