Standard syllabus
Optimization & linear programming · Undergraduate · Math
Topics
Linear programming
- Linear programming problems: standard form and geometry
- Feasible regions, vertices, and the fundamental theorem of LP
- Simplex method: pivoting, optimality, and termination
- Duality: weak and strong duality (statements)
- Sensitivity analysis and shadow prices (introduction)
Nonlinear optimization
- Unconstrained optimization: critical points and convexity
- Gradient descent and Newton's method for multivariable functions
- Constrained optimization: Lagrange multipliers
- Karush–Kuhn–Tucker (KKT) conditions (introduction)
- Convex sets and convex functions (definitions and examples)
Discrete and network optimization
- Integer programming and branch-and-bound (overview)
- Transportation and assignment problems
- Shortest path and minimum spanning tree problems
- Network simplex (introduction)
- Multi-objective optimization and Pareto efficiency (brief)
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$1,162 · Optimization & linear programming · 18 tutoring hrs
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