Chapter ONE

: Introduction 1.1 Introduction
1.2 Background of Study
1.3 Problem Statement
1.4 Objective of Study
1.5 Limitation of Study
1.6 Scope of Study
1.7 Significance of Study
1.8 Structure of the Research
1.9 Definition of Terms

Chapter TWO

: Literature Review 2.1 Overview of Multivariable Optimization
2.2 Historical Development in Optimization
2.3 Types of Optimization Algorithms
2.4 Applications of Multivariable Optimization
2.5 Constraints in Optimization Problems
2.6 Previous Studies on Multivariable Optimization with Constraints
2.7 Challenges in Multivariable Optimization
2.8 Emerging Trends in Optimization Research
2.9 Importance of Constraints in Optimization
2.10 Future Directions in Multivariable Optimization Research

Chapter THREE

: Research Methodology 3.1 Research Design
3.2 Data Collection Methods
3.3 Sampling Techniques
3.4 Data Analysis Procedures
3.5 Experimental Setup
3.6 Validation of Results
3.7 Ethical Considerations
3.8 Research Limitations

Chapter FOUR

: Discussion of Findings 4.1 Analysis of Data
4.2 Interpretation of Results
4.3 Comparison of Findings with Existing Literature
4.4 Implications of Findings
4.5 Recommendations for Practice
4.6 Recommendations for Future Research
4.7 Strengths and Weaknesses of the Study
4.8 Contributions to the Field of Optimization

Chapter FIVE

: Conclusion and Summary