The convex feasibility problem (CFP) is to find a member of the intersection of finitely many closed convex sets in Euclidean space. When the intersection is empty, one can minimize a proximity function to obtain an approximate solution to the problem. The split feasibility problem (SFP) and the split equality problem (SEP) are generalizations of the CFP. The approximate SFP (ASFP) and approxim...

Knowing the fact that the main weakness of the most standard methods including k-means and hierarchical data clustering is their sensitivity to initialization and trapping to local minima, this paper proposes a modification of convex data clustering  in which there is no need to  be peculiar about how to select initial values. Due to properly converting the task of optimization to an equivalent...

this paper uses integrated data envelopment analysis (dea) models to rank all extreme and non-extreme efficient decision making units (dmus) and then applies integrated dea ranking method as a criterion to modify genetic algorithm (ga) for finding pareto optimal solutions of a multi objective programming (mop) problem. the researchers have used ranking method as a shortcut way to modify ga to d...

Hybrid automata are well-studied formal models for dynamical systems. However, the analysis of hybrid automata is extremely difficult, and even state-of-the-art tools can only analyze systems with few continuous variables and simple dynamics. Because the reachability problem for general hybrid automata is undecidable, we give a path-oriented reachability analysis procedure for a class of nonlin...

In this paper, we study the split-feasibility problem in Hilbert spaces by using the projected reflected gradient algorithm. As applications, we study the convex linear inverse problem and the split-equality problem in Hilbert spaces, and we give new algorithms for these problems. Finally, numerical results are given for our main results.

In this paper, we study the link between a Chance-Constrained optimization Problem (CCP) and its sample counterpart (SP). SP has a finite number, say N , of sampled constraints. Further, some of these sampled constraints, say k, are discarded, and the final solution is indicated by x∗N,k. Extending previous results on the feasibility of sample convex optimization programs, we establish the feas...

The aim is to reconstruct a signal function x ∈ L2 if the phase of the Fourier transform x̂ and some additional a-priori information of convex type are known. The problem can be described as a convex feasibility problem. We solve this problem by different Fejér monotone iterative methods comparing the results and discussing the choice of relaxation parameters. Since the a-priori information is p...

This paper addresses the problem of locating an acoustic source using a sensor network in a distributed manner, i.e., without transmitting the full data set to a central point for processing. This problem has been traditionally addressed through the maximum likelihood framework or nonlinear least squares. These methods, even though asymptotically optimal under certain conditions, pose a difficu...

We consider a class of convex feasibility problems where the constraints that describe the feasible set are loosely coupled. These problems arise in robust stability analysis of large, weakly interconnected systems. To facilitate distributed implementation of robust stability analysis of such systems, we propose two algorithms based on decomposition and simultaneous projections. The rst algorit...

We analyse the behaviour of the newly introduced cyclic Douglas–Rachford algorithm for finding a point in the intersection of a finite number of closed convex sets. This work considers the case in which the target intersection set is possibly empty. 1. Preliminaries and Notation Throughout we assume H is a (real) Hilbert space with inner product 〈·, ·〉 and induced norm ‖ · ‖. We use → (resp. w....