Lectures related to Dognion's Theorem

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.

Covers semi-definite programming and optimization over positive semidefinite cones.

Variational Problems: Convexity and Coercivity

Explores variational problems, emphasizing convexity and coercivity conditions in functionals with integral side constraints.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Optimization Problems: Path Finding and Portfolio Allocation

Covers optimization problems in path finding and portfolio allocation.

Linear Programming: Weighted Bipartite Matching

Covers linear programming, weighted bipartite matching, and vertex cover problems in optimization.

Newtonian Potential: Bounded Domains

Explores Newtonian potential in bounded domains, discussing its conditions and properties.

Geodesic Convexity: Theory and Applications

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Optimization Methods: Theory Discussion

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

Optimal Transport: Rockafellar Theorem

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Mathematical Recursion: Induction and Recursion

Covers the principle of mathematical induction for proving propositions true for all positive integers.

Linear Programming: Optimization and Duality

Introduces linear programming, optimization, and duality concepts with a focus on the simplex method and practical examples.

Cutset Formulation: MST Problem

Explores the cutset formulation for the MST Problem and Gomory Cutting Planes method.

Elementary Algebra: Numeric Sets

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Proofs: Direct and Indirect Methods

Covers examples of direct and indirect proofs in mathematics.

Demonstration of Theorem

Covers the demonstration of a theorem regarding the minimum and maximum of a function.

Linear Programming Basics

Introduces linear programming basics, including optimization problems, cost functions, simplex algorithm, geometry of linear programs, extreme points, and degeneracy.

Proof of Strong Duality

Covers the proof of strong duality in optimization problems and provides examples of Rayleigh quotient optimization.

KKT and Convex Optimization

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