CMPSC 200 02 G MATLAB Optimization with fminsearch | Finding Local and Global Minima

Описание: CMPSC 200: MATLAB Optimization with fminsearch | Finding Local and Global Minima

Mastering the fminsearch function is a key skill for numerical optimization in MATLAB. In this tutorial, Joseph Mahoney demonstrates how to use this powerful built-in tool to find the minimum of a function without needing to calculate its derivative. This lesson is essential for students in CMPSC 200 and anyone performing engineering data analysis or scientific computing.

The video begins with an introduction to the fminsearch syntax. Unlike basic optimization methods, fminsearch can handle both scalar and multivariate functions, making it a robust choice for complex problems. You will learn about the two primary arguments: the function handle and the initial guess. We also discuss how to capture two outputs: the location (x value) where the minimum occurs and the actual function value at that point.

A significant portion of this lesson is dedicated to the challenges of local versus global optimization. Using a practical mathematical example, we demonstrate how an initial guess can cause the algorithm to get stuck in a local minimum. We show how to test multiple start points to ensure you have found the true global minimum. Furthermore, we cover a clever trick for finding the maximum of a function by using fminsearch on the negative of the function and then negating the resulting output.

Finally, we walk through a visual demonstration. You will see how to define a function with parameters, perform the optimization, and then use the scatter command to mark the discovered peaks and valleys on a plot using custom markers. By the end of this video, you will be able to apply fminsearch to your own engineering models with confidence.

Key Topics Explained:

1. Introduction to fminsearch: A derivative-free method for finding function minima.
2. Function Handles and Parameters: Passing constants into your optimization routine.
3. Initial Guess Sensitivity: Understanding how the starting point affects the result.
4. Local vs Global Minima: Avoiding suboptimal solutions in multimodal functions.
5. Finding Maxima: Techniques for negating functions to find the highest point.
6. Multivariate Optimization: A brief look at handling vectors and multivariable inputs.
7. Visual Verification: Using the scatter command to plot optimization results.

Timestamps:

00:00 Introduction to fminsearch and basic syntax
00:41 Understanding the two outputs of fminsearch
01:08 Multivariate capabilities and vector handling
01:46 How to find the maximum value of a function
02:16 Using function handles and passing parameters
02:41 Revisiting the example function and parameters
04:14 Finding the global minimum with an initial guess
05:40 Getting stuck in a local minimum with a poor guess
06:48 Technique for finding the global maximum
07:53 Capturing and correcting the maximum value output
08:49 Demonstrating local maxima vs global maxima
09:47 Visualizing results with the scatter command
10:50 Final plot with optimization markers

Resources and Links:

For more MATLAB tutorials, practice problems, and course materials, visit the official JMM MATLAB site: https://sites.google.com/view/jmm-mat...

For additional information on engineering projects and academic updates, visit: https://sites.google.com/view/jmmahoney/

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