Second Order Conic Programming
If the objective function or constraint condition contains nonlinear function, this kind of programming problem is called nonlinear programming problem. Second order conic programming (SOCP) is a common nonlinear programming problem, which has a wide range of application fields and practical significance. It researchs on problems include design, combinatorial optimization, finance, game theory, economics and many other fields.
For a vector space V and its subset C, if the product ax of any point X and any positive number a in subset C still belongs to subset C, then C is called a cone. (by definition, a cone is always unbounded.)
if any two points x and y in a cone C , for any two positive numbers a and b in,it has
Conic optimization is a generalization of linear optimization, allowing constraints of the type
A conic quadratic optimization is a problem of the following form:
subject to the constraints
and — the lower and upper bounds on constraints, and — the lower and upper bounds on variables.
where the domain restriction,
There are two standard forms of second-order cones:
Rotated quadratic cone