ML without tears

Tag: math

  • Lagrangian multipliers, normal cones and KKT optimality conditions

    We consider constrained optimization problems of the kind: where the feasibility region is a polytope, i.e., is the set of such that: where are real matrices of size and , respectively, and are column vectors. Equivalently, we can rewrite (1) as: where are the -th row of and , respectively, and denotes the scalar product. In this post we…

  • Get real! Solving a complex-value linear system using real arithmetic

    Consider a linear system of complex-valued equations of the kind , where are complex square and rectangular matrices, respectively, and is the unknown complex matrix. To compute , a natural option is to use any algorithm available in the literature initially conceived for real systems, such as Gauss elimination, LU/Cholesky decomposition, and translate its operations to complex arithmetic. However, there may…