A convex optimization problem is defined by two ingredients:
• The objective function, which is a real-valued
• The … See more

The following problem classes are all convex optimization problems, or can be reduced to convex optimization problems via simple transformations:
• Linear programming problems are the simplest co… See more

The following are useful properties of convex optimization problems:
• every local minimum is a global minimum;
• the optimal set is convex;
• if the objective function is strictly convex, then the problem has at mos… See more

The convex programs easiest to solve are the unconstrained problems, or the problems with only equality constraints. As the equality constraints are all linear, they can be eliminated with linear algebra and integrated i… See more

Consider a convex minimization problem given in standard form by a cost function and inequality constraints for . Then the domain is:
The Lagrangian function for the problem is
For each p… See more