This paper investigates the linear feasibility problem (LFP), which plays a fundamental role in image reconstruction, especially in applications such as computed tomography and signal processing. The goal is to find a point in the intersection of a finite collection of convex sets defined by linear constraints. We provide a structured overview and comparison of existing orthogonal projection-based iterative methods for solving LFPs, including sequential, simultaneous, and block-iterative algorithms. While these methods have been studied individually in the literature, our work highlights their theoretical underpinnings, practical performance, and convergence properties in a unified framework. We also revisit and refine known convergence theorems, discussing their assumptions and implications in the context of real-world reconstruction problems. The novelty of this study lies in its comprehensive synthesis of algorithmic strategies along with a critical analysis of their relative strengths, limitations, and applicability. This work aims to clarify the landscape of projection methods for LFPs and to guide the selection or development of more effective reconstruction techniques in practice.

Using the concept of eta-convex functions as generalization of convex functions, we inquiry about the relation between minimization problem and Kuhn-Tucker problem with new settings and give sucient and necessary optimality condition. Also the relation between minimization problem and it's Mond-Weir dual problem in convex case is investigated.

Application of the network equivalent concept for external system representation for power system transient analysis is well known. However, the challenge to utilize an equivalent network, approximated by a rational function, is to guarantee the passivity of the corresponding model. In this regard, special techniques are required to enforce the passivity of the equivalent model through a post processing approach that minimizes its impact on the original model characteristics. In this paper, the passivity is enforced by expressing the problem in terms of a convex optimization problem that guarantees the global optimal solution. The convex optimization problem is efficiently solved by recently developed numerical interior–point methods. This passivity enforcement is also global which indicates that the passivity enforcement in one region does not lead to passivity violation in other regions.

In this paper, we present two methods to find the strictly efficient and weakly efficient points of multi-objective programming (MOP) problems in which their objective functions are pseudo-convex and their feasible sets are polyhedrons. The obtained efficient solutions in these methods are the extreme points. Since the pseudo-convex functions are quasi-convex as well, therefore the presented methods can be used to find efficient solutions of the (MOP) problem with the quasi-convex objective functions and the polyhedron feasible set. Two experimental examples are presented.

The aim of this paper is to establish sequential necessary and sufficient approximate optimality conditions for a constrained convex vector mini-mization problem without any constraint qualifications, characterizing the approximate proper and weak efficient solutions. The constraints are de-scribed by mappings taking values in different preorder vector spaces. Our approach is based essentially on the sequential approximate subdifferential calculus rule for the sums of a finite family of cone convex mappings. To illustrate our main result, an application to multiobjective fractional pro-gramming problem is given. Finally, we present an important subclass of such problems showing the applicability of the obtained conditions.

The aim of present paper is to study a constrained programming with generalized α − univex fuzzy mappings. In this paper we introduce the concepts of α − univex, α − preunivex, pseudo α − univex and α − unicave fuzzy mappings, and we discover that α − univex fuzzy mappings are more general than univex fuzzy mappings. Then, we discuss the relationships of generalized α − univex fuzzy mappings and get some properties. In the last, we derive necessary and suffcient Karush-Kuhn-Tucker conditions and its dual problems with generalized differentiable α − univex fuzzy mappings for fuzzy constrained programming problem.