DSOS and SDSOS optimization: more tractable alternatives to sum of squares and semidefinite optimization

AA Ahmadi, A Majumdar - SIAM Journal on Applied Algebra and Geometry, 2019‏ - SIAM
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 …

Solving natural conic formulations with Hypatia. jl

C Coey, L Kapelevich… - INFORMS Journal on …, 2022‏ - pubsonline.informs.org
Many convex optimization problems can be represented through conic extended
formulations (EFs) using only the small number of standard cones recognized by advanced …

Sum-of-squares optimization without semidefinite programming

D Papp, S Yildiz - SIAM Journal on Optimization, 2019‏ - SIAM
We propose a homogeneous primal-dual interior-point method to solve sum-of-squares
optimization problems by combining nonsymmetric conic optimization techniques and …

Optimal self-concordant barriers for quantum relative entropies

H Fawzi, J Saunderson - SIAM Journal on Optimization, 2023‏ - SIAM
Quantum relative entropies are jointly convex functions of two positive definite matrices that
generalize the Kullback–Leibler divergence and arise naturally in quantum information …

Exploiting structure in quantum relative entropy programs

K He, J Saunderson, H Fawzi - arxiv preprint arxiv:2407.00241, 2024‏ - arxiv.org
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 …

Performance enhancements for a generic conic interior point algorithm

C Coey, L Kapelevich, JP Vielma - Mathematical Programming …, 2023‏ - Springer
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 …

Efficient implementation of interior-point methods for quantum relative entropy

M Karimi, L Tuncel - INFORMS Journal on Computing, 2024‏ - pubsonline.informs.org
Quantum relative entropy (QRE) programming is a recently popular and challenging class of
convex optimization problems with significant applications in quantum computing and …

Exploiting constant trace property in large-scale polynomial optimization

NHA Mai, JB Lasserre, V Magron, J Wang - ACM Transactions on …, 2022‏ - dl.acm.org
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 …

Error bounds, facial residual functions and applications to the exponential cone

SB Lindstrom, BF Lourenço, TK Pong - Mathematical programming, 2023‏ - Springer
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 …

Duality of sum of nonnegative circuit polynomials and optimal SONC bounds

D Papp - Journal of Symbolic Computation, 2023‏ - Elsevier
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 …