Chapter 8
Cone Programming (cvxopt.solvers)

In this chapter we consider convex optimization problems of the form

minimize  (1∕2)xTPx + qTx
subject to Gx ≼  h
          Ax = b.

The linear inequality is a generalized inequality with respect to a proper convex cone. It may include componentwise vector inequalities, second-order cone inequalities, and linear matrix inequalities. The main solvers are conelp() and coneqp(), described in sections 8.1 and 8.2. The function conelp() is restricted to problems with linear cost functions, but can detect primal and dual infeasibility. The function coneqp() solves the general quadratic problem, but requires the problem to be primal and dual feasible. For convenience (and backward compatibility), simpler interfaces to these function are also provided that handle pure linear programs, quadratic programs, second-order cone programs, and semidefinite programs. These are described in sections 8.38.6. In section 8.7 we explain how custom solvers can be implemented that exploit structure in cone programs. The last two sections describe optional interfaces to external solvers, and the algorithm parameters that control the cone programming solvers.

 8.1 Linear Cone Programs
 8.2 Quadratic Cone Programs
 8.3 Linear Programming
 8.4 Quadratic Programming
 8.5 Second-Order Cone Programming
 8.6 Semidefinite Programming
 8.7 Exploiting Structure
 8.8 Optional Solvers
 8.9 Algorithm Parameters