CONVERGENCE OF MANN’S ALTERNATING PROJECTIONS IN CAT() SPACES

We study the convex feasibility problem in$\text{CAT}(\unicode[STIX]{x1D705})$spaces using Mann’s iterative projection method. To do this, we extend Mann’s projection method in normed spaces to$\text{CAT}(\unicode[STIX]{x1D705})$spaces with$\unicode[STIX]{x1D705}\geq 0$, and then we prove the$\unicode[STIX]{x1D6E5}$-convergence of the method. Furthermore, under certain regularity or compactness conditions on the convex closed sets, we prove the strong convergence of Mann’s alternating projection sequence in$\text{CAT}(\unicode[STIX]{x1D705})$spaces with$\unicode[STIX]{x1D705}\geq 0$.

Convergence Theorems for Hierarchical Fixed Point Problems and Variational Inequalities

This paper deals with a modi fied iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under certain approximate assumptions of mappings and parameters. As a special case, this projection method solves some quadratic minimization problem. It should be noted that the proposed method can be regarded as a generalized version of Wang and Xu (2013), Ceng et al. (2011), Sahu et al. (2012), and many other authors.

The Optimized Iterative Projection Method to Determine the Width of an Arbitrary 3D Object

The problem to determine the width of a 3D object is involved in many engineering fields. This paper presents an optimized iterative projection method to solve this problem. In this way, the 3D width problem is turned into a 2D width problem, simplifying the solving process greatly. Furthermore, several improving strategies are addressed to reduce the amount of calculation and enhance the executing efficiency of the iterative projection approach. Experiments of models and point sets are also given to show the prominent performance of the proposed algorithm.

THREE-STEP PROJECTION METHOD FOR GENERAL VARIATIONAL INEQUALITIES

In this paper, we suggest and analyze a new three-step iterative projection method for solving general variational inequalities in conjunction with a descent direction. We prove that the new method is globally convergent under suitable mild conditions. An example is given to illustrate the advantage and efficiency of the proposed method.

GLOBAL CONVERGENCE OF RTLSQEP: A SOLVER OF REGULARIZED TOTAL LEAST SQUARES PROBLEMS VIA QUADRATIC EIGENPROBLEMS

The total least squares (TLS) method is a successful approach for linear problems if both the matrix and the right hand side are contaminated by some noise. In a recent paper Sima, Van Huffel and Golub suggested an iterative method for solving regularized TLS problems, where in each iteration step a quadratic eigenproblem has to be solved. In this paper we prove its global convergence, and we present an efficient implementation using an iterative projection method with thick updates.