Primal-dual Optimization: Fundamentals

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KKT for convex problems and Slater's CQ

Covers the KKT conditions and Slater's condition in convex optimization problems.

Convex Optimization: Exercises

Covers exercises on convex optimization, focusing on formulating and solving optimization problems using YALMIP and solvers like GUROBI and MOSEK.

Optimization Duality: Theory and Algorithms

Explores optimization duality, weak and strong duality, practical optimization algorithms, and challenges in nonconvex-concave problems.

Optimization Methods: Theory Discussion

Explores optimization methods, including unconstrained problems, linear programming, and heuristic approaches.

Linear Programming Duality

Explores the concept of duality in linear programming and its practical implications in optimization.

Gradient Descent Methods: Theory and Computation

Explores gradient descent methods for smooth convex and non-convex problems, covering iterative strategies, convergence rates, and challenges in optimization.

Optimization Problems: Path Finding and Portfolio Allocation

Covers optimization problems in path finding and portfolio allocation.

Lagrangian Duality: Theory and Applications

Explores Lagrangian duality in convex optimization, discussing strong duality, dual solutions, and practical applications in second-order cone programs.

Primal-dual Optimization: Algorithms and Convergence

Explores primal-dual optimization algorithms for convex-concave minimax problems, discussing convergence properties and applications.

KKT and Convex Optimization

Covers the KKT conditions and convex optimization, discussing constraint qualifications and tangent cones of convex sets.