Core Concepts
Algorithm for linearly constrained convex optimization using algebraic transformation.
Abstract
This paper introduces an interior point algorithm for solving linearly constrained convex optimization problems. The algorithm utilizes a parametric algebraic transformation to determine descent directions efficiently. The study concludes with a detailed analysis of the convergence and complexity of the proposed algorithm, highlighting its polynomial complexity bounds. Various extensions and applications of this method in different mathematical programs are discussed, showcasing its versatility and efficiency.
Stats
Polynomial complexity bounds achieved by the algorithm.
Function ψ(t) = √t used in determining descent directions.
Accuracy parameter ǫ > 0 for convergence analysis.
Update parameter θ = 1/e2r√n for optimal performance.