Optimization in Models

Mathematical Modeling · Axiom Academy

Discover how mathematical models help us find the best solutions to real-world problems Optimization is everywhere. Every day, you make decisions trying to achieve the best outcome given your constraints. Mathematical optimization formalizes this process. Click on the landscape to explore how we find optimal solutions. Click Start Search to watch the optimizer explore the landscape. Notice how it can get stuck at local optima! Anatomy of an Optimization Problem Every optimization problem has three essential components. Click each one to understand how they work together. Minimize cost: f(x) = total production cost Maximize profit: f(x) = revenue - expenses Minimize error: f(x) = sum of squared residuals Production quantities for each product Investment amounts in each asset Parameters in a machine learning model Physical constraints: 0 x capacity Requirements: demand must be met Optimization problems come in many flavors, each requiring different solution techniques. Click each type to learn about its characteristics. Optimization drives decisions across every industry and discipline. Click each example to discover how optimization models shape our world.

This is the written version of the interactive lesson above. See the full Mathematical Modeling course.