Relaxed inertial methods for solving the split monotone variational inclusion problem beyond co-coerciveness

Abstract

We study the split monotone variational inclusion problem in two real Hilbert spaces. Combining the inertial and relaxation techniques with the proximal contraction algorithm, we propose two new methods for solving this problem without the usual co-coerciveness assumption on the associated operators.

Keywords:

• Contraction method
• Lipschitz continuous
• monotone opearator
• proximal algorithm
• relaxed inertial method
• split monotone variational inclusion problem

2010 Mathematics Subject Classifications:

• 47H09
• 47H10
• 49J20
• 49J40

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The second author was partially supported by the Israel Science Foundation [grant 820/17], by the Fund for the Promotion of Research at the Technion and by the Technion General Research Fund.