Optimization & linear programming
Undergraduate · Math
Syllabus focus
Standard syllabus · STEM / applied
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Topics typically covered
Standard syllabus
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)
STEM / applied
Applications and software
- Production planning and resource allocation models
- Portfolio optimization (Markowitz model, introduction)
- Scheduling and blending problems in industry
- Solver use in Excel, Python (SciPy), or GAMS
- Case studies in logistics and supply chain
Algorithms and computation
- Interior-point methods (conceptual overview)
- Quadratic programming applications
- Nonlinear least squares and curve fitting
- Heuristic methods: simulated annealing and genetic algorithms (intro)
- Robustness and infeasibility diagnosis in large models
Notes
Topics reflect common optimization and linear programming syllabi at US colleges and universities. Some programs emphasize OR/IE applications; others focus on the mathematical foundations of convex optimization.