This thesis is in Computational Geometry. Computational Geometry is a subfield of Computer Science that deals with problems of a geometric nature that arise in application domains such as Computer Graphics, Robotics, Geographic Information Systems (GIS), and Molecular Biology. More specifically, in this thesis we conduct research in Computational Geometry in the context of (Geometric) Facility ...

Machine learning models often rely on sparsity, low-rank, orthogonality, correlation, or graphical structure. The structure of interest in this chapter is geometric, specifically the manifold of positive definite (PD) matrices. Though these matrices recur throughout the applied sciences, our focus is on more recent developments in machine learning and optimization. In particular, we study (i) m...

Drawing ideas from differential geometry and optimization, this thesis presents novel parameterization-based framework to address optimization problems formulated on a differentiable manifold. The framework views the manifold as a collection of local coordinate charts. It involves successive parameterizations of a manifold, carrying out optimization of the local cost function in parameter space...

1. Abstract Structural topology optimization often leads to slender structures which are sensitive to geometric imperfections such as the misplacement of material. A robust approach is therefore presented in order to take into account material misplacement in topology optimization problems. A probabilistic approach to robust optimization is followed. Spatially varying geometric imperfections ar...

Geometric programming is an important class of optimization problems that enable practitioners to model a large variety of real-world applications, mostly in the field of engineering design. In many real life optimization problem multi-objective programming plays a vital role in socio economical and industrial optimizing problems. In this paper we have discussed the basic concepts and principle...

this article is devoted to the simultaneous optimization of shape and topology of shell structures. the optimum shape is obtained together with the optimum layout for the reinforcement layers at the both sides of the shell surface. to solve this problem the finite element method is employed. it is assumed that each element is comprised of a porous media with microscopic rectangular voids where ...

The chapter aims to give computational algorithm to solve a multiobjective non-linear programming problem using Neutrosophic geometric programming technique. As the Neutrosophic optimization technique utilizes degrees of truth-membership, falsity-membership and indeterminacy-membership functions, we made a study of correspondence among those membership functions to see its impact on optimizatio...

The main purpose of the present work is multi-objective shape optimization of a projectile tip for impacting and normal penetrating. Velocity drop, weight and inner volume of projectile have been considered as three conflicting objective functions.  For this purpose, at the first step, finite element modeling was done using ABAQUS/Explicit and projectile penetration was examined in different ge...

One primary problem in shape optimization of structures is making a robust link between design model (geometric description) and analysis model. This paper investigates the potential of Isogeometric Analysis (IGA) for solving this problem. The generic framework of shape optimization of structures is presented based on Isogeometric analysis. By discretization of domain via NURBS functions, the a...

Fitting of data points by parametric curves and surfaces is demanded in many scientific fields. In this paper we review and analyze existing least squares orthogonal distance fitting techniques in a general numerical optimization framework. Two new geometric variant methods (GTDM and CDM) are proposed. The geometric meanings of existing and modified optimization methods are also revealed.