Optimization and Operations Research
Explore objectives and convexity; algorithms and constraints; discrete decisions and multiple objectives. Concepts and connections are available independently of video coverage.
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Convex optimization
Minimizing a convex function on a convex feasible set makes local minima global.
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Convex functions
A convex function lies below chords connecting points on its graph.
Convex sets
Every segment joining two points of a convex set stays inside the set.
Optimization
Derivatives help identify candidate extrema; endpoints, domain restrictions and the distinction between local and global extrema must also be checked.
Gradient descent
Iterates move opposite the gradient; step-size and smoothness conditions control convergence.
Newton optimization
Gradient and Hessian information form a local quadratic step, often with globalization safeguards.
Knowledge connections
- Convex functions · Related · Map context
- Optimization · Related · Map context
- Convex sets · Prerequisite · Map context
- Convex functions · Prerequisite · Map context