Optimization

What is Convex Optimization?

Convex optimization is a special class of mathematical optimization problems, which includes least-squares and linear programming problems.

There are many advantages to recognizing or formulating a problem as a convex optimization problem. First, the problem can be solved reliably and efficiently, using interior-point methods or other special methods for convex optimization. There are also theoretical or conceptual advantages of formulating a problem as a convex optimization problem.

Mathematical Optimization

An optimization problem has the form:

$\begin{aligned} minimize & f_{0} (x) \\ subject to & f_{i} (x) \leq b_{i}, i = 1, \dots, m \end{aligned}$

Here the vector $x = (x_{1}, \dots, x_{n})$ is the optimization variable of the problem, the function $f_{0} : R^{n} \to R$ is the objective function, $f_{i} R^{n} \to R$ are the (inequality) constraint functions, and the constants $b_{1}, \dots, b_{m}$ are the limits, or bounds, for the constraints.

We consider families or classes of optimization problems, characterized by particular forms of the objective and constraint functions. The optimization problem is a linear program if the objective and constraint functions $f_{0}, \dots, f_{m}$ are linear.

Jethro's Braindump

Optimization

What is Convex Optimization?

Mathematical Optimization

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