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DSOS and SDSOS optimization: more tractable alternatives to sum of squares and semidefinite optimization
In recent years, optimization theory has been greatly impacted by the advent of sum of
squares (SOS) optimization. The reliance of this technique on large-scale semidefinite …
squares (SOS) optimization. The reliance of this technique on large-scale semidefinite …
Solving natural conic formulations with Hypatia. jl
Many convex optimization problems can be represented through conic extended
formulations (EFs) using only the small number of standard cones recognized by advanced …
formulations (EFs) using only the small number of standard cones recognized by advanced …
Sum-of-squares optimization without semidefinite programming
We propose a homogeneous primal-dual interior-point method to solve sum-of-squares
optimization problems by combining nonsymmetric conic optimization techniques and …
optimization problems by combining nonsymmetric conic optimization techniques and …
Optimal self-concordant barriers for quantum relative entropies
Quantum relative entropies are jointly convex functions of two positive definite matrices that
generalize the Kullback–Leibler divergence and arise naturally in quantum information …
generalize the Kullback–Leibler divergence and arise naturally in quantum information …
Exploiting structure in quantum relative entropy programs
Quantum relative entropy programs are convex optimization problems which minimize a
linear functional over an affine section of the epigraph of the quantum relative entropy …
linear functional over an affine section of the epigraph of the quantum relative entropy …
Performance enhancements for a generic conic interior point algorithm
In recent work, we provide computational arguments for expanding the class of proper cones
recognized by conic optimization solvers, to permit simpler, smaller, more natural conic …
recognized by conic optimization solvers, to permit simpler, smaller, more natural conic …
Efficient implementation of interior-point methods for quantum relative entropy
Quantum relative entropy (QRE) programming is a recently popular and challenging class of
convex optimization problems with significant applications in quantum computing and …
convex optimization problems with significant applications in quantum computing and …
Exploiting constant trace property in large-scale polynomial optimization
We prove that every semidefinite moment relaxation of a polynomial optimization problem
(POP) with a ball constraint can be reformulated as a semidefinite program involving a …
(POP) with a ball constraint can be reformulated as a semidefinite program involving a …
Error bounds, facial residual functions and applications to the exponential cone
We construct a general framework for deriving error bounds for conic feasibility problems. In
particular, our approach allows one to work with cones that fail to be amenable or even to …
particular, our approach allows one to work with cones that fail to be amenable or even to …
Duality of sum of nonnegative circuit polynomials and optimal SONC bounds
Circuit polynomials are polynomials with properties that make it easy to compute sharp and
certifiable global lower bounds for them. Consequently, one may use them to find certifiable …
certifiable global lower bounds for them. Consequently, one may use them to find certifiable …