The Kantorovich theorem and interior point methods

DOI10.1007/s10107-003-0501-8zbMath1059.90137OpenAlexW2006960705MaRDI QIDQ1769068

Florian A. Potra

Publication date: 17 March 2005

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10107-003-0501-8

zbMATH Keywords

Linear complementarity problemInterior point algorithmKantorovich TheoremPath-following

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Newton-type methods (49M15) Numerical computation of solutions to systems of equations (65H10) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33)

Related Items

Kantorovich's majorants principle for Newton's method, Local convergence analysis of inexact Newton method with relative residual error tolerance under majorant condition in Riemannian manifolds, Robust semi-local convergence analysis for inexact Newton method, Wiener-Hopf and spectral factorization of real polynomials by Newton's method, A Superquadratic Variant of Newton's Method, A robust Kantorovich's theorem on the inexact Newton method with relative residual error tolerance, Unnamed Item, Kantorovich's theorem on Newton's method for solving generalized equations under the majorant condition, A weak Kantorovich existence theorem for the solution of nonlinear equations, Kantorovich's Theorem on Newton's Method for Solving Strongly Regular Generalized Equation, Nonlinear Fredholm integral equations and majorant functions, Expanding the applicability of the Kantorovich's theorem for solving generalized equations using Newton's method, Concerning the convergence of Newton's method and quadratic majorants, Concerning the semilocal convergence of Newton's method and convex majorants

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on Newton type iterative methods
• Error bounds for Newton's iterates derived from the Kantorovich theorem
• A unified derivation of several error bounds for Newton's process
• A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions
• A polynomial-time algorithm, based on Newton's method, for linear programming
• Sharp error bounds for Newton's process
• An updated version of the Kantorovich theorem for Newton's method
• A unified approach to interior point algorithms for linear complementarity problems: A summary
• Unified complexity analysis for Newton LP methods
• New convergence criteria for the Newton-Kantorovich method and some applications to nonlinear integral equations
• Convergence of Newton-like methods for singular operator equations using outer inverses
• Primal-dual algorithms for linear programming based on the logarithmic barrier method
• A Kantorovich theorem for the structured PSB update in Hilbert space.
• Conditioning of semidefinite programs
• Historical developments in convergence analysis for Newton's and Newton-like methods
• Interior-point methods
• A unified convergence theory for Newton-type methods for zeros of nonlinear operators in Banach spaces
• Kantorovich's theorem on Newton's method in Riemannian manifolds
• On solution of nonlinear singular integral equations with shift in generalized Hölder space
• Primal-dual target-following algorithms for linear programming
• An application of the Kantorovich theorem to nonlinear finite element analysis
• A Mathematical View of Interior-Point Methods in Convex Optimization
• A GENERALIZED THEOREM OF MIRANDA AND THE THEOREM OF NEWTON–KANTOROVICH
• On a general iterative scheme for newton-type methods
• A kantorovich-type theorem for inexact newton methods
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• The Kantorovich Theorem with Optimal Error Bounds
• On the asymptotics of meromorphic solutions for nonlinear Riemann–Hilbert problems
• An Approach to The Numerical Verification of Solutions for Nonlinear Elliptic Problems With Local Uniqueness
• Multipoint Super-Halley Type Approximation Algorithms in Banach Spaces
• Rigorous verification of chaotic behaviour of maps using validated shadowing
• Optimal Error Bounds for the Newton–Kantorovich Theorem
• The Newton-Kantorovich Theorem
• The Kantorovich Theorem for Newton's Method
• On the Kantorovich Hypothesis for Newton’s Method
• Asymptotic expansions and a new numerical algorithm of the algebraic Riccati equation for multiparameter singularly perturbed systems