The Newton modified barrier method for QP problems

DOI10.1007/BF02206827zbMath0848.90099OpenAlexW2038435941MaRDI QIDQ1915923

Roman A. Polyak, Aaron Melman

Publication date: 3 November 1996

Published in: Annals of Operations Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02206827

zbMATH Keywords

Lagrange multiplierscondition numbersecond-order optimality conditionsmodified barrier functionshot startNewton MBF methodrelaxation operator

Mathematics Subject Classification ID

Abstract computational complexity for mathematical programming problems (90C60) Quadratic programming (90C20)

Related Items (7)

Nonlinear rescaling as interior quadratic prox method in convex optimization ⋮ The Legendre Transformation in Modern Optimization ⋮ A resolução do problema de despacho ótimo de reativos pelo método da função lagrangiana-barreira relaxada ⋮ Support vector machine via nonlinear rescaling method ⋮ 1.5-\(Q\)-superlinear convergence of an exterior-point method for constrained optimization ⋮ Primal-dual nonlinear rescaling method with dynamic scaling parameter update ⋮ An exterior point polynomial-time algorithm for convex quadratic programming

Cites Work

• Theoretical efficiency of a shifted-barrier-function algorithm for linear programming
• Unified complexity analysis for Newton LP methods
• Modified barrier functions (theory and methods)
• On the classical logarithmic barrier function method for a class of smooth convex programming problems
• Nonlinear rescaling and proximal-like methods in convex optimization
• An \(O(n^ 3L)\) primal interior point algorithm for convex quadratic programming
• On projected newton barrier methods for linear programming and an equivalence to Karmarkar’s projective method
• A duality theorem for non-linear programming
• Path-Following Methods for Linear Programming
• The convergence of a modified barrier method for convex programming
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