Solving second-order conic systems with variable precision
Felipe Cucker, Javier Pe\~na, Vera Roshchina
TL;DR
This paper introduces an interior-point method for solving second-order conic feasibility problems that operates with finite precision arithmetic, providing bounds on the computational effort and precision needed.
Contribution
It presents a novel interior-point algorithm that explicitly accounts for finite precision arithmetic, including bounds on operations and precision requirements.
Findings
The algorithm successfully determines feasibility with finite precision arithmetic.
Bounds on the number of arithmetic operations are established.
The required precision levels are explicitly quantified.
Abstract
We describe and analyze an interior-point method to decide feasibility problems of second-order conic systems. A main feature of our algorithm is that arithmetic operations are performed with finite precision. Bounds for both the number of arithmetic operations and the finest precision required are exhibited.
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Taxonomy
TopicsAdvanced Optimization Algorithms Research · Polynomial and algebraic computation · Numerical Methods and Algorithms