Solving Natural Conic Formulations with Hypatia.jl

DOI10.1287/ijoc.2022.1202OpenAlexW3182400646MaRDI QIDQ5058009

Juan Pablo Vielma, Chris Coey, L. Kapelevich

Publication date: 1 December 2022

Published in: INFORMS Journal on Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.01136

zbMATH Keywords

interior point methodsconic optimizationextended formulations

Mathematics Subject Classification ID

Mathematical programming (90Cxx)

Related Items

Hypatia.jl, Sum of squares generalizations for conic sets, Error bounds, facial residual functions and applications to the exponential cone, Optimal Self-Concordant Barriers for Quantum Relative Entropies, Performance enhancements for a generic conic interior point algorithm, Entropy constraints for ground energy optimization

Uses Software

• CSDP
• SDPA
• CVXOPT
• CVX
• Mosek
• ECOS
• CVXPY
• Julia
• JuMP
• SCS
• GitHub
• Convex.jl
• Pajarito
• alfonso
• MathOptInterface.jl

Cites Work

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• CVXPY
• Julia
• SCS
• GitHub
• Convex.jl
• MathOptInterface.jl
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• Disciplined geometric programming
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• Lectures on Modern Convex Optimization
• CVXPY: A Python-Embedded Modeling Language for Convex Optimization
• Julia: A Fresh Approach to Numerical Computing
• Extended Formulations in Mixed-Integer Convex Programming
• Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
• Barrier Functions in Interior Point Methods
• Self-Scaled Barriers and Interior-Point Methods for Convex Programming
• CSDP, A C library for semidefinite programming
• Sum-of-Squares Optimization without Semidefinite Programming
• Implementation and evaluation of SDPA 6.0 (Semidefinite Programming Algorithm 6.0)
• Alfonso: Matlab Package for Nonsymmetric Conic Optimization
• MathOptInterface: A Data Structure for Mathematical Optimization Problems
• Towards non-symmetric conic optimization
• Solving Conic Optimization Problems via Self-Dual Embedding and Facial Reduction: A Unified Approach
• JuMP: A Modeling Language for Mathematical Optimization