An inertial projection and contraction algorithm for pseudomonotone variational inequalities without Lipschitz continuity

ABSTRACT

In this paper, we present an inertial projection and contraction algorithm (IPCA for short) for variational inequality problems (VIP for short) without Lipschitz continuity of the underlying mapping in Euclidean space. To obtain a larger step, the next iterate point of IPCA is generated by projecting the current iterate point onto a selected half-space, which is selected from finite half-spaces (one half-space can strictly separate the current iterate point from the solution set of VIP and other half-spaces are all contain the solution set of VIP) and has the largest distance to the current iterate point. Moreover, a new initial step-size strategy is used to accelerate IPCA. The global convergence of the sequence generated by IPCA is established. Numerical experiments show that IPCA can accelerate PCA both from the number of iterations point of view and the number of projections point of view.

KEYWORDS:

• Variational inequalities
• half-space projection
• inertial technique
• initial step-size
• Armijo linesearch

MATHEMATICS SUBJECT CLASSIFICATIONS (2020):

• 47J20
• 49J40
• 90C33

Disclosure statement

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

Notes

1 The procedure to select $t_i$ can be performed in a parallel way. Hence, its computational cost can also be ignored.