On the complexity of analyticity in semi-definite optimization

DOI10.1016/j.aam.2024.102670arXiv2301.06257OpenAlexW4391708191WikidataQ128162657 ScholiaQ128162657MaRDI QIDQ6118356

Ali Mohammad Nezhad, Saugata Basu

Publication date: 21 March 2024

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2301.06257

zbMATH Keywords

quantifier eliminationcentral pathNewton-Puiseux theoremreal univariate representationsemi-definite optimization

Mathematics Subject Classification ID

Semidefinite programming (90C22) Interior-point methods (90C51) Semialgebraic sets and related spaces (14P10)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bounding the radii of balls meeting every connected component of semi-algebraic sets
• The central curve in linear programming
• Rational algebraic curves. A computer algebra approach
• A power series method for computing singular solutions to nonlinear analytic systems
• On the analyticity properties of infeasible-interior point paths for monotone linear complementarity problems
• Infeasible-interior-point paths for sufficient linear complementarity problems and their analyticity
• Limiting behavior of weighted central paths in linear programming
• An exact duality theory for semidefinite programming and its complexity implications
• Irreducibility criterion for germs of analytic functions of two complex variables
• Analyticity of the central path at the boundary point in semidefinite programming
• Analysis of infeasible-interior-point paths arising with semidefinite linear complementarity problems
• Generating and measuring instances of hard semidefinite programs
• Numerical algebraic geometry and semidefinite programming
• Asymptotic behavior of the central path for a special class of degenerate SDP problems
• On the curvature of the central path of linear programming theory
• Computing singular solutions to nonlinear analytic systems
• A Strongly Polynomial Rounding Procedure Yielding a Maximally Complementary Solution for $P_*(\kappa)$ Linear Complementarity Problems
• Semidefinite optimization
• The Nonlinear Geometry of Linear Programming. I Affine and Projective Scaling Trajectories
• The Nonlinear Geometry of Linear Programming. II Legendre Transform Coordinates and Central Trajectories
• All Algebraic Functions Can Be Computed Fast
• Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results
• Interior Point Trajectories in Semidefinite Programming
• Limiting Behavior of the Derivatives of Certain Trajectories Associated with a Monotone Horizontal Linear Complementarity Problem
• Superlinear Convergence of a Symmetric Primal-Dual Path Following Algorithm for Semidefinite Programming
• Algorithms in Real Algebraic Geometry: A Survey
• On the Convergence of the Central Path in Semidefinite Optimization
• Semidefinite Optimization and Convex Algebraic Geometry
• A polynomial-time complexity bound for the computation of the singular part of a Puiseux expansion of an algebraic function
• Irreducibility testing over local fields
• Basic Algebraic Geometry 1
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
• Singular Points of Complex Hypersurfaces. (AM-61)
• On the Central Path of Semidefinite Optimization: Degree and Worst-Case Convergence Rate
• On the identification of the optimal partition for semidefinite optimization
• Algorithms in real algebraic geometry

This page was built for publication: On the complexity of analyticity in semi-definite optimization