Descent methods with computational errors in Banach spaces

ABSTRACT

Given a Lipschitz convex and coercive objective function on a Banach space, we revisit the class of regular vector fields introduced in our previous work on descent methods. Taking into account computational errors, we study the behaviour of the values of the objective function for the process generated by a regular vector field and show that if the computational errors are small enough, then the values of the objective function become close to its infimum.

KEYWORDS:

• Banach space
• complete metric space
• convex function
• descent method
• iterative process

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 49M37
• 90C25
• 90C30

Acknowledgements

Both authors are grateful to the referees for many helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author was partially supported by the Israel Science Foundation (Grant No. 820/17), by the Fund for the Promotion of Research at the Technion and by the Technion General Research Fund.