Lagrangian Duality: Theory and Applications

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Explores optimization problems in standard form, convex optimization, and optimality criteria.

Covers sensitivity analysis in linear programming, focusing on optimal solutions and their sensitivities to changes.

Covers the application of the two-phase Simplex algorithm to solve linear programming problems.

Covers Farkas' lemma, exploring the relationship between linear programs and the conditions for its validity.

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

Explores the formulation of the auxiliary problem in linear optimization and its role in optimal decision-making.

Explores dual cones, generalized inequalities, SDP duality, and KKT conditions in convex optimization.

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

Explores self-dual cones in convex optimization and their applications in various optimization problems.

Explains the process of finding an initial Basic Feasible Solution for linear optimization problems using the Simplex Algorithm.