Extension of the Barzilai–Borwein Method for Quadratic Forms in Finite Euclidean Spaces

DOI10.1080/01630560902841179zbMath1161.49034OpenAlexW2081796602MaRDI QIDQ3630406

William La Cruz

Publication date: 29 May 2009

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: http://www.informaworld.com/smpp/./content~db=all~content=a910367563

zbMATH Keywords

quadratic formEuclidean spaceBarzilai-Borwein methodlinear matrix equations

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Quadratic programming (90C20) Linear-quadratic optimal control problems (49N10)

Related Items (1)

Minimization of quadratic forms using the Drazin-inverse solution

Uses Software

• Lyap

Cites Work

• The iterative solution of the matrix equation \(XA+BX+C=0\)
• Krylov-subspace methods for the Sylvester equation
• On the numerical solution of \(AX-XB=C\)
• Two-Point Step Size Gradient Methods
• Krylov Subspace Methods for Solving Large Lyapunov Equations
• Nonmonotone Spectral Methods for Large-Scale Nonlinear Systems
• On the structure of balanced and other principal representations of SISO systems
• On the Barzilai and Borwein choice of steplength for the gradient method
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Spectral residual method without gradient information for solving large-scale nonlinear systems of equations
• Block descent methods and hybrid procedures for linear systems
• Block Krylov subspace methods for solving large Sylvester equations

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