Background and Objectives: Object tracking in video streams is one of the issues in machine vision that has many applications. Depending on the type of the object, the number of objects and other inputs used in tracking, object tracking is divided into several different categories. Multi-object tracking in a camera network is one of the most complex types of object tracking. In this type of tracking, the goal of the algorithm is to extract the persistent trace of several objects moving simultaneously in a wide area that is monitored by a network of cameras. This type of tracking is often done in two steps. In the first step, the traces of each object in each camera is called tracklets are extracted. Then, the persistent trace of the objects are obtained by associating the extracted tracklets of all cameras in the monitored wide area. Here, we introduce a novel Variational approach based on the deep features to associate the tracklets. Methods: For this purpose a Variational model with multiphase level set representation is introduced. The persistent trace of all objects are obtained by optimizing the proposed Variational model. The proposed Variational model is optimized by employing the Euler-Lagrange equation. CNN and deep learning are used to extract the deep features of appearance and motion of objects. Here, a ResNet50 network that is pre-trained on ImageNet and a transformer neural network which is trained with motion parameters of tracklets such as acceleration and orientation change rate are used for extracting deep features. Results: The multiphase model using deep features presented in this paper provide 9% better results than the multiphase model without deep features based on TCF and FS metrics and 8% better results based on MT metric. Conclusion: The results on the three well-known datasets which are real and a synthesized dataset show that the proposed model takes competitive performance, while using less extra context information of the camera network and objects, compared to the other proposed methods. The evaluations show the quality of the proposed model in solving complex problems using the minimum required initial knowledge.

In this paper we prove that if X is a Banach space, then for every lower semi-continuous bounded below function f; there exists a ('1; '2)-convex function g; with arbitrarily small norm, such that f + g attains its strong minimum on X: This result extends some of the well-known varitional principles as that of Ekeland [On the Variational principle, J. Math. Anal. Appl. 47 (1974) 323{ 353], that of Borwein-Preiss [A smooth Variational principle with applications to subdi erentiability and to di erentiability of convex functions, Trans. Amer. Math. Soc. 303 (1987) 517{527] and that of Deville-Godefroy-Zizler [Un principe variationel utilisant des fonctions bosses, C. R. Acad. Sci. (Paris). Ser. I 312 (1991) 281{286] and [A smooth Variational principle with applications to Hamilton-Jacobi equations in in nite dimensions, J. Funct. Anal. 111 (1993) 197{212].

In this paper, we consider different types of generalized vector Variational-like inequalities and study the relationships between their  olutions . We study the general forms of Stampacchia and Minty type vector Variational inequalities for bifunctions and establish the existence of their solutions in the setting of topological vector spaces. We extend these vector Variational inequalities for the Clarke’s sub differential of non-differentiable locally Lipschitz functions and prove the existence of their solutions. As applications, we establish some existence results for a solution of the vector optimization problem by using Stampacchia and Minty type vector Variational inequalities.

In this paper, we examine the perturbed absolute value Variational inequalities (PAVVI), a new class of Variational inequalities. For the (PAVVI), some new merit functions are established. We develop the error bounds for (PAVVI) using these merit functions. The results presented here recapture a number of previously established findings in the relevant fields because (PAVVI) include Variational inequalities, the absolute value complementarity problem, and systems of absolute value equations as special cases.

In this paper, we propose a split nonconvex Variational inequality problem which is a natural extension of split convex Variational inequality problem in two different Hilbert spaces. Relying on the prox-regularity notion, we introduce and establish the convergence of an iterative method for the new split nonconvex Variational inequality problem. Further, we also establish the convergence of an iterative method for the split convex Variational inequality problem. The results presented in this paper are new and different form the previously known results for nonconvex (convex) Variational inequality problems. These results also generalize, unify, and improve the previously known results of this area.

This paper presents improved analytical method for predicting deflection of reinforced concrete beams. This approach considers stiffness of steel and concrete separately. A number of diverse analytical models have been proposed by various researchers aimed at accurately predicting deflection of reinforced concrete bent elements. In this paper energy model is formed and varied. Deflection is determined from the potential energy model. To establish the validity of the proposed model correlation of analytical solution of existing models are conducted. Variation model solutions generally show very good agreement with results obtained other analytical methods.

It is well known that the quasi Variational inequalities are equivalent to the fixed point problems. We this equivalent alternative formulation to discuss the existence of a solution of quasi Variational inequalities under some mild conditions Since the quasi Variational inequalities include Variational inequalities, implicit complementarity problems and optimization problems as special cases, results proved in this paper continue to hold these problems. This shows that results proved in this paper can be viewed as an important and significant improvement and refinement of the previous results.