Template Function cutting_plane_feas

Function Documentation

template<typename Oracle, typename Space>
auto cutting_plane_feas(Oracle &&Omega, Space &&S, const Options &options = Options()) -> CInfo

Find a point in a convex set (defined through a cutting-plane oracle).

A function f(x) is convex if there always exist a g(x) such that f(z) >= f(x) + g(x)’ * (z - x), forall z, x in dom f. Note that dom f does not need to be a convex set in our definition. The affine function g’ (x - xc) + beta is called a cutting-plane, or a ``cut’’ for short. This algorithm solves the following feasibility problem: 

    find x
    s.t. f(x) <= 0,

A separation oracle asserts that an evalution point x0 is feasible, or provide a cut that separates the feasible region and x0.

Template Parameters

  • Oracle –

  • Space –

Parameters

  • Omega – [inout] perform assessment on x0

  • S – [inout] search Space containing x*

  • options – [in] maximum iteration and error tolerance etc.

Returns

Information of Cutting-plane method