Standard syllabus
Optimization & linear programming · Undergraduate · Math
Learning objectives from the Optimization & linear programming syllabus, grouped by unit. Click an objective for study materials.
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Optimization & Linear Programming — scope drawn from open optimization / LP materials (e.g. Boyd convex-optimization companion undergrad tracks) and typical US syllabi.
Linear programming
- Linear programming problems: standard form and geometry — Linear programming problems: standard form and geometry
- Feasible regions and vertices — Feasible regions and vertices
- The fundamental theorem of LP — The fundamental theorem of LP
- Simplex method — Simplex method
- Termination — Termination
- Duality: weak and strong duality (statements) — Duality: weak and strong duality (statements)
- Sensitivity analysis — Sensitivity analysis
- Shadow prices (introduction) — Shadow prices (introduction)
Nonlinear optimization
- Unconstrained optimization — Unconstrained optimization
- Convexity — Convexity
- Gradient descent — Gradient descent
- Newton's method for multivariable functions — Newton's method for multivariable functions
- Constrained optimization: Lagrange multipliers — Constrained optimization: Lagrange multipliers
- Karush–Kuhn–Tucker (KKT) conditions (introduction) — Karush–Kuhn–Tucker (KKT) conditions (introduction)
- Convex sets and convex functions (definitions and examples) — Convex sets and convex functions (definitions and examples)
Discrete and network optimization
- Integer programming — Integer programming
- Branch-and-bound (overview) — Branch-and-bound (overview)
- Transportation and assignment problems — Transportation and assignment problems
- Shortest path — Shortest path
- Minimum spanning tree problems — Minimum spanning tree problems
- Network simplex (introduction) — Network simplex (introduction)
- Multi-objective optimization — Multi-objective optimization
- Pareto efficiency (brief) — Pareto efficiency (brief)
Learning objectives
Click an objective for study materials.
Linear programming
- Linear programming problems: standard form and geometry — Linear programming problems: standard form and geometry
- Feasible regions and vertices — Feasible regions and vertices
- The fundamental theorem of LP — The fundamental theorem of LP
- Simplex method — Simplex method
- Termination — Termination
- Duality: weak and strong duality (statements) — Duality: weak and strong duality (statements)
- Sensitivity analysis — Sensitivity analysis
- Shadow prices (introduction) — Shadow prices (introduction)
Nonlinear optimization
- Unconstrained optimization — Unconstrained optimization
- Convexity — Convexity
- Gradient descent — Gradient descent
- Newton's method for multivariable functions — Newton's method for multivariable functions
- Constrained optimization: Lagrange multipliers — Constrained optimization: Lagrange multipliers
- Karush–Kuhn–Tucker (KKT) conditions (introduction) — Karush–Kuhn–Tucker (KKT) conditions (introduction)
- Convex sets and convex functions (definitions and examples) — Convex sets and convex functions (definitions and examples)
Discrete and network optimization
- Integer programming — Integer programming
- Branch-and-bound (overview) — Branch-and-bound (overview)
- Transportation and assignment problems — Transportation and assignment problems
- Shortest path — Shortest path
- Minimum spanning tree problems — Minimum spanning tree problems
- Network simplex (introduction) — Network simplex (introduction)
- Multi-objective optimization — Multi-objective optimization
- Pareto efficiency (brief) — Pareto efficiency (brief)
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Linear programming
Linear programming problems: standard form and geometry
Coming soon - Nonlinear optimization
Unconstrained optimization
Coming soon - Discrete and network optimization
Integer programming
Coming soon
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$1,162 · Optimization & linear programming · 18 tutoring hrs
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