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Here are two examples of linear programming problems. This one here is a minimization problem and this one here is a ...

You might have observed that when you solve a linear programming problem, you often end up with an optimal solution there is ...

Recall that the dual problem of this minimization problem is defined to be this linear programming problem here. There are a ...

The fundamental theorem of linear programming states the following: for any given linear programming problem, exactly one of ...

Recall the following result from linear algebra: a system of linear equations Ax = b is inconsistent (that is, has no solution) if and ...

Notice that x* satisfies this system of linear equations. But since the rank of this matrix is n, that means x* is the only solution to the ...

In OpenMDAO terms, your nonlinear system is your model or governing system of equations. Your linear system is a ...

If you're fitting a curve or surface to data and want to ever use gradient-based optimizers or Newton solvers, make sure to do it in a ...

We can turn these equations to linear inequalities if we want and apply the Fourier-Motzkin elimination, eliminating the variables ...

Multiobjective optimization is somewhat of a misnomer -- you actually have to have predefined weightings for each of the ...

This procedure can be applied repeatedly. So we can eliminate iteratively x_1 up to x_n until we get down to zero variable.

- The Linear Latent Growth Model is one of the simplest models for modeling effects of time that you can use in SEM and estimate ...

One of the most important steps in optimization is formulating well-posed and meaningful problems that you can interpret ...

Week 5: Lecture 10A: Extreme points and optimal solution of an LP.

I use iPhone 17 pro max→ https://amzn.to/3Vr1BB6 This short video provides a brief overview of the #linearschedulingmethod ...

When you have a coupled or implicit system, you must use a solver to converge that system. Take time to recognize those systems ...

Week 7: Lecture 13A: Farkas' lemma.

Fractals are complex, never-ending patterns created by repeating mathematical equations. Yuliya, a undergrad in Math at MIT, ...

05b: Solving a Linear Algebra Problem In MATLAB 05a-05b comprise a two-part demo on Linear Algebra. 05a: Converts a set of ...

Some insights I have on P=?NP and the logic satisfiability problem, with an emphasis on AI.