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And we let (P) denote this linear programming problem. Then the dual problem of (P) is the following linear programming problem.

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

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

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

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

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

Inferring inequalities using simple operations.

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

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

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

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 ...

And we know we worked with linear equations before, and we know that represents lines. But when we deal with three variables, ...

This is an audio version of the Wikipedia Article: https://en.wikipedia.org/wiki/Cutting-plane_method 00:03:16 1 Gomory's cut ...

Under the hood is a big bad ol' Mixed-Integer Linear Program (MILP) and the awesome HiGHS linear solver, and this series is ...

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

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.

Week 7: Lecture 13A: Farkas' lemma.

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