Displaying similar documents to “Penalty/barrier path-following in linearly constrained optimization”

A new diagonal quasi-Newton algorithm for unconstrained optimization problems

Mahsa Nosrati, Keyvan Amini (2024)

Applications of Mathematics

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We present a new diagonal quasi-Newton method for solving unconstrained optimization problems based on the weak secant equation. To control the diagonal elements, the new method uses new criteria to generate the Hessian approximation. We establish the global convergence of the proposed method with the Armijo line search. Numerical results on a collection of standard test problems demonstrate the superiority of the proposed method over several existing diagonal methods.

Nonlinear Rescaling Method and Self-concordant Functions

Richard Andrášik (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Nonlinear rescaling is a tool for solving large-scale nonlinear programming problems. The primal-dual nonlinear rescaling method was used to solve two quadratic programming problems with quadratic constraints. Based on the performance of primal-dual nonlinear rescaling method on testing problems, the conclusions about setting up the parameters are made. Next, the connection between nonlinear rescaling methods and self-concordant functions is discussed and modified logarithmic barrier...

Uniform Convergence of the Newton Method for Aubin Continuous Maps

Dontchev, Asen (1996)

Serdica Mathematical Journal

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* This work was supported by National Science Foundation grant DMS 9404431. In this paper we prove that the Newton method applied to the generalized equation y ∈ f(x) + F(x) with a C^1 function f and a set-valued map F acting in Banach spaces, is locally convergent uniformly in the parameter y if and only if the map (f +F)^(−1) is Aubin continuous at the reference point. We also show that the Aubin continuity actually implies uniform Q-quadratic convergence provided that...