Physics

Variational inequality

Operator (biology)

Lipschitz continuity

Relaxation (psychology)

Mathematics

Economic growth

Weak convergence

Transcription factor

Biology

Gene

Mathematical optimization

Subgradient method

Mathematical analysis

Inertial frame of reference

Psychology

Repressor

Economics

Chemistry

Convergence (economics)

Sequence (biology)

Computer science

Quantum mechanics

Monotonic function

Applied mathematics

Computer security

Genetics

Biochemistry

Hilbert space

Asset (computer security)

Social psychology

Journal of Scientific Computing

In this paper, we present two new relaxed inertial subgradient extragradient methods for solving variational inequality problems in a real Hilbert space. We establish the convergence of the sequence generated by these methods when the cost operator is quasimonotone and Lipschitz continuous, and when it is Lipschitz continuous without any form of monotonicity. The methods combine both the inertial and relaxation techniques in order to achieve high convergence speed, and the techniques used are quite different from the ones in most papers for solving variational inequality problems. Furthermore, we present some experimental results to illustrate the profits gained from the relaxed inertial steps.

Convergence of Relaxed Inertial Subgradient Extragradient Methods for Quasimonotone Variational Inequality Problems