Graduate Student Seminar

Ahamd Mousavi

Title

An inexact SQP method for equality constrained optimization

Abstract

We present an algorithm for large-scale equality constrained optimization. The method is based on a characterization of inexact sequential quadratic programming (SQP) steps that can ensure global convergence. Inexact SQP methods are needed for large-scale applications for which the iteration matrix cannot be explicitly formed or factored and the arising linear systems must be solved using iterative linear algebra techniques. We address how to determine when a given inexact step makes sufficient progress toward a solution of the nonlinear program, as measured by an exact penalty function. The method is globalized by a line search.

Cherre Jefferson

Title

Algebraic Coding Theory

Abstract

The effectiveness of cell phones, radios, fax machines, PCs and barcodes for which electronic digital information is transmitted from one machine to another heavily relies on the theory of Algebraic Coding. ACT (Algebraic Coding Theory) is the theory of transmitting information in the most effective manner and has no relation to secret codes. It was created in the 1940s to respond to the practical communication issues at the time. In fact, ACT is one of the most widely used applications of Mathematics, especially in this world today of immediate communication. The process of encoding messages into longer codes with redundancy which enables the receiving communication device to decode, detect and/or correct any errors created during transmission is called Forward Error Detection/Correction (FEDC). This research focuses on the explanation of the basic principles of FEDC. While exploring the various types of block codes, which is one of the three well known methods of FEDC, we also analyzed the efficiency of certain error correction codes by calculating the probability of successful decoding of a transmitted message. The Block Codes we decided to focus on are Repetition Codes and Linear Codes with an emphasis on Hamming Codes.