A convex optimization problem consists of either minimizing a convex objective or maximizing a concave objective over a convex feasible region.

Convex Optimization is a special case of mathematical optimization where the feasible region is convex and the objective is to either minimize a convex function or maximize a concave function. Linear Programming is a special case. Convex Optimization problems as a class are easier to solve numerically than general mathematical optimization problems.

The following problems are all convex minimization problems, or can be transformed into convex minimizations problems via a change of variables:

- Least squares
- Linear programming
- Convex quadratic minimization with linear constraints
- Quadratic minimization with convex quadratic constraints
- Conic optimization
- Geometric programming
- Second order cone programming
- Semidefinite programming
- Entropy maximization with appropriate constraints