Optimization Theory: Concepts, Methods, and Applications

Introduced by Polyak in 1966, the class of strongly quasiconvex functions includes some interesting nonconvex members, like the square root of the Euclidean norm or ratios with a nonnegative strongly convex numerator and a concave and positive denominator. In this talk, we survey the most relevant examples of strongly quasiconvex functions and results involving them available in the literature...

Providing the existence of an intersection point for a family of sets is commonly useful in many problems. Various studies have been done in this regard within the framework of KKM theory. The concept of weak KKM has been applied in some papers within this objective. In these results, the existence of a solution is often linked to certain closedness and compactness conditions that are not...

In this paper, we introduce and study a Halpern inertial method for solving the general
perturbed Krasnoselskii–Mann type algorithm in Hilbert space settings, where the underlying mapping is
quasi–nonexpansive. We discuss convergence analysis of the method under some mild assumptions on the
control sequences. We additionally present a numerical example to demonstrate the effectiveness of...

This work presents a new iterative scheme and establishes its convergence results to approximate the fixed points of nonexpansive mapping. In particular, we demonstrate effectiveness of our proposed iterative scheme in the image restoration process by formulating the problem as a split feasibility problem (SFP). A comparative analysis reveals that our scheme not only converges faster than some...

This study develops a compartmental model to characterize the transmission dynamics of the Hepatitis B virus (HBV) with two distinct viral strains. The basic reproduction number is derived via the next-generation matrix method, and three biologically relevant equilibria are identified and analyzed. To evaluate intervention policies, an optimal control problem is formulated with two...