Linearly Constrained Minimization

The linearly constrained minimization problem can be stated as follows:

\[\begin{split}\begin{array}{ll} \min_{x \in R^n} f(x)&\\ \text{subject to} & A_1x=b_1\\ &A_2x \le b_2\\ \end{array}\end{split}\]

where \(f:\mathcal{R}^n \to \mathcal{R}\) is a function, \(A_1\) and \(A_2\) are coefficient matrices, and \(b_1\) and \(b_2\) are vectors. If f(x) is linear, then the problem is a linear programming (LP) problem.

Function imsl.optimize.sparse_lp() uses an infeasible primal-dual interior-point method to solve sparse LP problems of all sizes. The constraint matrix is stored in sparse coordinate storage (SCS) or compressed sparse column (CSC) format.