In the last three decades, there has been extensive research activities on both the theory and the real applications of nonlinear and variational analysis, two closely related research fields in applied mathematics. They find various applications in many fields, ranging from science and engineering to economics and social sciences.

Recently, iterative methods – in particular, the methods with inertial terms – have been investigated extensively to find solutions of various nonlinear problems, such as variational inequalities, fixed-point problems, variational inclusions, etc. Many new results were established with projections in various spaces.

This Special Issue will focus on nonlinear and variational analysis, while also addressing the practical nature of the two fields. In addition to the strong focus in computational mathematics and operational research, a special emphasis will be given to scientific computing, the theory of numerical methods for solutions of various nonlinear equations, and applications of these fields. This Special Issue solicits high-quality original research articles as well as review articles addressing recent advances. We welcome theoretical, numerical, and experimental contributions.

Potential topics include but are not limited to the following:

• Fixed point theory, methods, and applications
• Equilibrium problems, variational inequalities
• Splitting methods, including backward-forward, ADMM and proximal methods
• Banach space theory and geometry
• Bregman operators
• Feasibility and split feasibility problems
• Convex/nonconvex, nonsmooth, and set-valued analysis
• Optimal control theory and methods
• Differential (including integral, delayed, impulsive) equations and dynamical systems
• Inverse problems and regularization methods