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Optimization

min

Optimization

Find the best solutions to mathematical problems

128Modules

7Units

Being rebuilt

This course is still in our original format. All the content is here and free to use, but it has not yet been through the rebuild that gives our newer courses their interactive animations and cleaner visuals — so you may hit some rough edges. Spot an error? Send us a note and we will fix it.

Recommended preparation

You will lean on multivariable calculus (Calculus 3) and linear algebra — gradients and matrices appear throughout.

Calculus 3 Linear Algebra (Matrices)

What is Optimization?INTRO

Optimization EverywhereINTRO

Types of Optimization ProblemsINTRO

Objective FunctionsLESSON

ConstraintsLESSON

Problem FormulationLESSON

Problem Formulation ExamplesEXAMPLE

Problem Formulation ToolACTIVITY

Formulation PracticePRACTICE

Feasible RegionsLESSON

Local vs Global OptimaLESSON

Identifying OptimaEXAMPLE

Identifying Optima PracticePRACTICE

Introduction to ConvexityLESSON

Existence and UniquenessLESSON

Resource AllocationREAL WORLD

Introduction SummarySUMMARY

Optimization Basics ReferenceREFERENCE

Introduction QuizQUIZ

What is Linear Programming?INTRO

LP ApplicationsINTRO

Standard FormLESSON

Graphical MethodLESSON

Graphical LP ExamplesEXAMPLE

Graphical LP ToolACTIVITY

Graphical Method PracticePRACTICE

Corner Point TheoremLESSON

Introduction to SimplexLESSON

Simplex AlgorithmLESSON

Simplex Method ExamplesEXAMPLE

Simplex TableauxLESSON

Simplex PracticePRACTICE

Two-Phase SimplexLESSON

LP SolverACTIVITY

Duality TheoryLESSON

Dual Simplex MethodLESSON

Sensitivity AnalysisLESSON

Manufacturing OptimizationREAL WORLD

Integer Programming IntroductionLESSON

Linear Programming SummarySUMMARY

Linear Programming ReferenceREFERENCE

Linear Programming QuizQUIZ

Unconstrained ProblemsINTRO

Calculus Review for OptimizationINTRO

First-Order Necessary ConditionsLESSON

Second-Order ConditionsLESSON

Gradient DescentLESSON

Gradient Descent ExamplesEXAMPLE

Gradient Descent VisualizerACTIVITY

Gradient Descent PracticePRACTICE

Step Size SelectionLESSON

Line Search MethodsLESSON

Newton's MethodLESSON

Newton's Method ExamplesEXAMPLE

Newton's Method PracticePRACTICE

Convergence RatesLESSON

Machine Learning OptimizationREAL WORLD

Quasi-Newton MethodsLESSON

BFGS AlgorithmLESSON

Conjugate Gradient MethodLESSON

Unconstrained Optimization SummarySUMMARY

Unconstrained Optimization ReferenceREFERENCE

Unconstrained Optimization QuizQUIZ

Constrained ProblemsINTRO

Types of ConstraintsINTRO

Equality ConstraintsLESSON

Lagrange MultipliersLESSON

Lagrange Multiplier ExamplesEXAMPLE

Lagrange Multipliers PracticePRACTICE

Inequality ConstraintsLESSON

Active ConstraintsLESSON

KKT ConditionsLESSON

KKT Condition ExamplesEXAMPLE

KKT Conditions PracticePRACTICE

Penalty MethodsLESSON

Barrier MethodsLESSON

Constrained OptimizerACTIVITY

Interior Point MethodsLESSON

Sequential Quadratic ProgrammingLESSON

Engineering DesignREAL WORLD

Constrained Optimization SummarySUMMARY

Constrained Optimization ReferenceREFERENCE

Constrained Optimization QuizQUIZ

What is Convex Optimization?INTRO

Why Convexity MattersINTRO

Convex SetsLESSON

Convex Sets PracticePRACTICE

Convex FunctionsLESSON

Convex Functions PracticePRACTICE

Operations Preserving ConvexityLESSON

Convexity CheckerACTIVITY

Convex Optimization ProblemsLESSON

Convex Problem ExamplesEXAMPLE

Quasiconvex FunctionsLESSON

Lagrangian DualityLESSON

Duality ExamplesEXAMPLE

Strong DualityLESSON

Semidefinite ProgrammingLESSON

Conic ProgrammingLESSON

Signal ProcessingREAL WORLD

Convex Optimization SummarySUMMARY

Convex Optimization ReferenceREFERENCE

Convex Optimization QuizQUIZ

Discrete OptimizationINTRO

Combinatorial ProblemsINTRO

Integer ProgrammingLESSON

Integer Programming ExamplesEXAMPLE

Integer Programming PracticePRACTICE

Branch and BoundLESSON

Branch and Bound VisualizerACTIVITY

Cutting Plane MethodsLESSON

Traveling Salesman ProblemLESSON

TSP ExamplesEXAMPLE

Knapsack ProblemLESSON

Assignment ProblemLESSON

Scheduling ApplicationsREAL WORLD

Network OptimizationLESSON

Combinatorial PracticePRACTICE

Heuristic MethodsLESSON

MetaheuristicsLESSON

Discrete Optimization SummarySUMMARY

Discrete Optimization ReferenceREFERENCE

Discrete Optimization QuizQUIZ

Problem Solving GuideSUMMARY

Optimization Master ReferenceREFERENCE

Complete Formula SheetFORMULA SHEET

Algorithm CatalogFORMULA SHEET

Comprehensive Optimization TestQUIZ