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Table of Contents

Chapter 1: Introduction
1.1 Background of the Study
1.2 Problem Statement
1.3 Objectives of the Study
1.4 Limitations of the Study
1.5 Scope of the Study

Chapter 2: Literature Review
2.1 Overview of Mathematical Optimization
2.2 Linear Programming
2.3 Convex Optimization
2.4 Applications of Linear Programming and Convex Optimization

Chapter 3: Research Methodology
3.1 Data Collection Methods
3.2 Data Analysis Techniques
3.3 Mathematical Models and Formulations

Chapter 4: Discussion of Findings
4.1 Analysis of Results
4.2 Comparison of Linear Programming and Convex Optimization
4.3 Interpretation of Findings

Chapter 5: Conclusion and Summary
5.1 Summary of Findings
5.2 Contributions to Knowledge
5.3 Recommendations for Future Research

Overview of Thesis: Mathematical Optimization: Linear Programming and Convex Optimization

Mathematical optimization is a field of study that deals with finding the best solutions to problems within given constraints. Two commonly used techniques in mathematical optimization are linear programming and convex optimization.

Linear programming involves optimizing a linear objective function subject to linear equality and inequality constraints. It is widely used in various fields such as economics, engineering, and operations research. Convex optimization, on the other hand, deals with optimizing convex functions subject to convex constraints. It is a more general form of optimization that includes linear programming as a special case.

This thesis aims to explore the principles and applications of linear programming and convex optimization. The literature review will discuss the theoretical foundations of these techniques and their practical implications. The research methodology will outline the data collection methods and analysis techniques used in the study. The discussion of findings will present the results of applying linear programming and convex optimization to a real-world problem, highlighting the strengths and limitations of each approach. Finally, the conclusion and summary will summarize the key findings, contributions to knowledge, and recommendations for future research in the field of mathematical optimization.

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