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Adjustment of the scaling parameter of Dai-Kou type conjugate gradient methods with application to motion control

Mahbube Akbari, Saeed Nezhadhosein, Aghile Heydari (2024)

Applications of Mathematics

We introduce a new scaling parameter for the Dai-Kou family of conjugate gradient algorithms (2013), which is one of the most numerically efficient methods for unconstrained optimization. The suggested parameter is based on eigenvalue analysis of the search direction matrix and minimizing the measure function defined by Dennis and Wolkowicz (1993). The corresponding search direction of conjugate gradient method has the sufficient descent property and the extended conjugacy condition. The global...

All-at-once preconditioning in PDE-constrained optimization

Tyrone Rees, Martin Stoll, Andy Wathen (2010)

Kybernetika

The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound...

An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints

Michael Kieweg, Yuri Iliash, Ronald H. W. Hoppe, Michael Hintermüller (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator...

An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints

Michael Hintermüller, Ronald H.W. Hoppe, Yuri Iliash, Michael Kieweg (2007)

ESAIM: Control, Optimisation and Calculus of Variations

We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator...

Currently displaying 121 – 140 of 200