Linear Optimization: Directional Derivatives

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Introduction to Optimization and Operations Research

Covers fundamental concepts of optimization and operations research, exploring real-world examples and key topics over a semester.

Linear Constraints: Elimination of Variables

Explains linear constraints and variable elimination in optimization problems, illustrating the process step by step.

Optimization with Constraints

Covers the optimization with constraints and the KKT theorem.

Linear Independence and Basis

Explains linear independence, basis, and matrix rank with examples and exercises.

Energy System Modeling: Optimization and Performance Indicators

Explores energy system modeling using optimization techniques and performance indicators.

Optimization Programs: Piecewise Linear Cost Functions

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

Optimization with Constraints: KKT Conditions

Covers the optimization with constraints, focusing on the Karush-Kuhn-Tucker (KKT) conditions.

Simplex Algorithm: Solution on a Vertex

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

Optimization: Mathematical Principles and Algorithms

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

Geodesic convexity: why, and what we need

Explores geodesic convexity and its extension to optimization on manifolds, emphasizing the preservation of the key fact that local minima imply global minima.