A modified double inertial subgradient extragradient algorithm for non-monotone variational inequality with applications

Abstract

This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized half-space and a self-adaptive step-size rule which works without prior knowledge of the Lipschitz constant of the operator. We establish a weak convergence result for a variational inequality involving a non-monotone cost operator along with weak and strong convergence results for quasi-monotone and strongly pseudo-monotone operators, respectively. Under a simplified framework, linear convergence of the proposed method is also discussed. Additionally, we provide some numerical experiments to demonstrate the effectiveness of our iterative algorithm compared to previously established algorithms in solving real-world applications. Finally, we carry out a sensitivity analysis of our algorithm to demonstrate its effectiveness across various parameter settings.

Figures (7)

• Figure 1: Comparison of algorithms for network equilibrium flow.
• Figure 2: Sensitivity analysis of Algorithm 4.1 (MDISEM) in network equilibrium flow with $\mu= 0.6$ and varying values of $\sigma$ and $\beta$.
• Figure 3: Comparison of algorithms for Nash-Cournot problem
• Figure 4: Sensitivity analysis of Algorithm 4.1 (MDISEM) in Nash-Cournot problem with $\mu= 0.6$ and varying values of $\sigma$ and $\beta$.
• Figure 5: Comparison of algorithms in image restoration problem

Theorems & Definitions (22)

• Definition 3.1
• Lemma 3.1
• Lemma 3.2
• Lemma 3.3
• Lemma 3.4
• Remark 4.1
• Lemma 4.1
• proof
• Lemma 4.2
• proof