Optimality Conditions in Linear Optimization

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Optimization Programs: Piecewise Linear Cost Functions

Covers the formulation of optimization programs for minimizing piecewise linear cost functions.

Convex Optimization Tutorial: KKT Conditions

Explores KKT conditions in convex optimization, covering dual problems, logarithmic constraints, least squares, matrix functions, and suboptimality of covering ellipsoids.

Simplex Algorithm: Solution on a Vertex

Explores the simplex algorithm and how optimal solutions can be found on vertices of constraint polyhedra.

Networks: Formulation

Explains the formulation of network optimization problems to minimize transportation costs.

Integer Programs: Optimization and Constraints

Explores integer programs, nonconvex optimization, constraints, and geometric aspects of linear programming for optimal solutions.

Optimisation Problem: Solving by FM

Covers the modelling and optimization of energy systems, focusing on solving optimization problems with constraints and variables.

ALM with Inequalities: Next Steps in Optimization

Explores the Augmented Lagrangian Method with equality and inequality constraints in optimization, emphasizing the importance of slack variables.

Lagrangian Duality: Convex Optimization

Explores Lagrangian duality in convex optimization, transforming problems into min-max formulations and discussing the significance of dual solutions.

Linear Optimization: Directional Derivatives

Explores directional derivatives in linear optimization and their impact on objective functions.

Optimization: Mathematical Principles and Algorithms

Covers mathematical principles and algorithms of optimization, using real-world examples and Python implementation.