A quadratically convergent method for linear programming

DOI10.1016/0024-3795(91)90278-5zbMath0731.65050OpenAlexW2090806510WikidataQ114852073 ScholiaQ114852073MaRDI QIDQ808185

Maria Cristina Recchioni, Stefano Herzel, Francesco Zirilli

Publication date: 1991

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(91)90278-5

zbMATH Keywords

linear programminginitial value problemquadratic convergence\(A\)-stabilityEuler's methodKarmarkar's projective algorithm

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Linear programming (90C05) Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (9)

Stable barrier-projection and barrier-Newton methods in linear programming ⋮ A Faster Method For Computing Karmarkar's Projections For Large Number of Constraints ⋮ Maximum likelihood estimation of the Heston stochastic volatility model using asset and option prices: an application of nonlinear filtering theory ⋮ Box-constrained multi-objective optimization: A gradient-like method without ``a priori scalarization ⋮ An interior point algorithm for global optimal solutions and KKT points ⋮ Maximum likelihood estimation of the parameters of a system of stochastic differential equations that models the returns of the index of some classes of hedge funds ⋮ A Cooperative Sensor Network: Optimal Deployment and Functioning ⋮ Monotone variable-metric algorithm for linearly constrained nonlinear programming ⋮ Determining a stable relationship between hedge fund index HFRI-Equity and S&P 500 behaviour, using filtering and maximum likelihood

Uses Software

• DAFNE

Cites Work

• A new polynomial-time algorithm for linear programming
• Homotopy techniques in linear programming
• A multiplicative barrier function method for linear programming
• Computing Karmarkar projections quickly
• On projected newton barrier methods for linear programming and an equivalence to Karmarkar’s projective method
• On the average number of steps of the simplex method of linear programming
• A differential-equations algorithm for nonlinear equations
• A variable-metric variant of the Karmarkar algorithm for linear programming
• The Nonlinear Geometry of Linear Programming. I Affine and Projective Scaling Trajectories
• Power Series Variants of Karmarkar-Type Algorithms
• Multistep Methods with Variable Matrix Coefficients
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