Lecture
Optimization with Constraints
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Quasi-newton optimization
Covers gradient line search methods and optimization techniques with an emphasis on Wolfe conditions and positive definiteness.
Optimization with Constraints: KKT Conditions
Covers optimization with constraints using KKT conditions and matrix invertibility in numerical analysis.
Optimal Control: KKT Conditions
Explores optimal control and KKT conditions for non-linear optimization with constraints.
Optimization Methods
Covers optimization methods without constraints, including gradient and line search in the quadratic case.
Optimization Methods
Covers unconstrained and constrained optimization, optimal control, neural networks, and global optimization methods.
Nonlinear Optimization
Covers line search, Newton's method, BFGS, and conjugate gradient in nonlinear optimization.
Numerical analysis
Covers advanced numerical analysis topics including deep neural networks and optimization methods.
Numerical methods: runge-kutta
Covers the Runge-Kutta method and its variations, discussing error minimization and stability in non-linear systems.
Optimal Control: Unconstrained and Constrained Problems
Explores optimal control in unconstrained and constrained problems, emphasizing the importance of sparsity.
Convergence of the method
Covers the convergence of the method and the importance of adapting time steps for accurate approximations.