This paper presents a novel bilevel Optimization approach for a nonlinear partial differential equation. The approach aims to enhance the quality of image denoising  by estimating certain parameters within this equation. Our work deals with both analytical and numerical results. Analytically, we establish the existence of a solution to the bilevel Optimization problem and apply the Alternating Direction Method of Multipliers algorithm to approximate this solution. Furthermore, the method fine-tunes the restoration process, effectively reducing noise while preserving crucial image features. Finally, numerical results validate the performance of our method, surpassing traditional denoising approaches. This research makes an important contribution to image restoration, paving the way for high-quality practical applications.

Bilevel Optimization is proposed when the objective problem has two decision makers with different hierarchies. In such cases, the lower level decision is embedded within the higher-level constraints. Micro and macro decision making of transportation are considered as hierarchal problems, On the one hand, user’ s decision tends to choose lower cost, and the other hand is transportation company’ s to maximize its benefit. This paper’ s aim is to provide a review on research and methods with different concerns for modeling and solving bilevel problems in last three decades. In addition, the latest application of this kind of Optimization is presented in aerospace transport issues. This paper also introduces the classic and heuristic algorithms for solving bilevel Optimization.

Decentralized planning has long been recognized as an important decision making problem. Many approaches based on the concepts of large-scale system decomposition have generally lacked the ability to model the type of truly independent subsystem which often exist in practice. Multilevel programming models partition control over decision variable among ordered levels within a hierarchical planning structure. This paper examines the special case of the multilevel liner programming problem, i.e. bilevel linear programming problem. Bilevel programming often represent an adequate tool for modeling non cooperative hierarchical decision processes, where one player optimizes over a subset of decision variables, while taking into account the independent reaction of the other player to his or course of action. Bilevel programming is an important area of current research stimulated by it's intrinsically very difficult nature and is still a little known technique, rarely used despite all it's potential capabilities. in this note a definition for a general bilevel programming some applications, geometric characterization and solution approaches are presented with some examples.

Bilevel linear programming is a decision making problem with a two-level decentralized organization. The “leader” is in the upper level and the “follower”, in the lower. Making a decision at one level affects that at the other one. In this paper, bilevel linear programming with inexact parameters has been studied and a method is proposed to solve a fuzzy bilevel linear programming using interval bilevel linear programming.

In this paper, recommended spiral passive micromixer was designed and simulated. spiral design has the potential to create and strengthen the centrifugal force and the secondary flow. A series of simulations were carried out to evaluate the effects of channel width, channel depth, the gap between loops, and flowrate on the micromixer performance. These features impact the contact area of the two fluids and ultimately lead to an increment in the quality of the mixture. In this study, for the flow rate of 25 μl/min and molecular diffusion coefficient of 1×10-10 m2/s, mixing efficiency of more than 90% is achieved after 30 (approximately one-third of the total channel length). Finally, the optimized design fabricated using proposed 3D printing method.

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.

Bilevel programming, a tool for modeling decentralized decision problem, consists of the objective of the leader at its first level and that of the follower at the second level. Bilevel programming has been proved to be an Np-hard problem. Numerous algorithms have been developed for solving bilevel programming problems. These algorithms lack the required efficiency for solving a real problem. In this paper, attempts have been made to develop an algorithm based Simulated Annealing (SA) Approach. This algorithm is efficient enough to find a near optimal solution. The proposed method is compared with the one developed by Mathieu et al [1] through application of both to a number of different problems.  

Bilevel programming, a tool for modeling decentralized decision problem, consists of the objective of the leader at its first level and that of the follower at the second level. Bilevel programming has been proved to be Np hard problem. Numerous algorithms have been developed for solving bilevel programming problem. These algorithms have not enough efficiency for solving a real problem. In this paper an attempt has been made to develop an algorithm based on Tabu Search (TS) approach. This algorithm can be efficient to finding a near optimal solution. In this paper, the proposed method and that of Mathieu and et.al [1] are also compared by solving different problems.