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7: Optimization

Last updated

Apr 23, 2021
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- 6.8: Characteristics of Real Ocean Waves
- 7.1: Introduction to Optimization

Franz S. Hover & Michael S. Triantafyllou
Massachusetts Institute of Technology via MIT OpenCourseWare

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7.1: Introduction to Optimization
What is optimization? Introduction to cost and parameter space.
7.2: Single-Dimension Continuous Optimization
Optimization of known and continuous single-variable functions, using the zero-derivative test and Newton's method.
7.3: Multi-Dimensional Continuous Optimization
Methods of finding the optimization of a multidimensional cost function that depends on more than one variable: steepest-descent, conjugate gradient, and Newton's second-order method.
7.4: Linear Programming
Optimization in cases where cost is a linear function of multiple parameters, comprising inequality and/or equality constraints.
7.5: Integer Linear Programming
The branch-and-bound method for solving optimization problems that involve continuous cost and constraint functions but allow only integer solutions.
7.6: Min-Max Optimization for Discrete Choices
The min-max method: finding the smallest normalized deviation from the peak performance across objectives, as a way to select the optimal solution in a situation which has multiple discrete candidates.
7.7: Dynamic Programming
Introduction to dynammic programming approach of solving optimization problems with a high number of unknowns, specifically focusing on shortest-path problems.
7.8: Solving Dynamic Programming on a Computer
Using the value iteration algorithm to efficiently solve shortest-path optimization problems with a computer.

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