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\contentsline {section}{\numberline {1}Introduction to Optimization and Control}{3}{section.1}%
\contentsline {section}{\numberline {2}Mathematical Optimization Foundations}{3}{section.2}%
\contentsline {subsection}{\numberline {2.1}Convex Optimization Theory}{3}{subsection.2.1}%
\contentsline {subsection}{\numberline {2.2}Gradient-Based Optimization Algorithms}{4}{subsection.2.2}%
\contentsline {section}{\numberline {3}Linear and Nonlinear Programming}{5}{section.3}%
\contentsline {subsection}{\numberline {3.1}Linear Programming and the Simplex Method}{5}{subsection.3.1}%
\contentsline {subsection}{\numberline {3.2}Constrained Optimization and KKT Conditions}{5}{subsection.3.2}%
\contentsline {section}{\numberline {4}Optimal Control Theory}{6}{section.4}%
\contentsline {subsection}{\numberline {4.1}Linear Quadratic Regulator (LQR)}{6}{subsection.4.1}%
\contentsline {subsection}{\numberline {4.2}Kalman Filtering and State Estimation}{7}{subsection.4.2}%
\contentsline {section}{\numberline {5}Robust Control and Uncertainty}{8}{section.5}%
\contentsline {section}{\numberline {6}Conclusion and Applications}{8}{section.6}%
\contentsline {subsection}{\numberline {6.1}Optimization Insights}{8}{subsection.6.1}%
\contentsline {subsection}{\numberline {6.2}Control Theory Applications}{8}{subsection.6.2}%
\contentsline {subsection}{\numberline {6.3}Computational Considerations}{8}{subsection.6.3}%
\contentsline {section}{\numberline {A}Algorithm Summary}{9}{appendix.A}%