Smoothconcave

SparseLP_old(c, polyhedron, zeps, max_warm_start)

Compute the sparsest solution of a linear program (LP)

\[\begin{split}min ~& c^T x \\ s.t. ~& S x = b \\ ~& lb \leq x \leq ub\end{split}\]

USAGE:

[result_tab, error_code, nb_warm_start, z] = SparseLP_old (c, polyhedron, zeps, max_warm_start)

INPUTS:

• c – n x 1 linear objective coefficient vector

• polyhedron – Structure describing the feasible polyhedron, with fields:

  • .Aeq - equality constraint matrix (Aeq*x = beq)

  • .beq - equality constraint right hand side vector

  • .Ain - inequality constraint matrix (Ain*x <= bin)

  • .bin - inequality constraint right hand side vector

  • .lb - lower bound vector

  • .ub - upper bound vector

• zeps – Precision threshold below which a value is considered to be zero

• max_warm_start – Maximum number of warm starts allowed for the sparsity-seeking (Theta L0) iterations

OUTPUTS:

• result_tab – Vector of the number of nonzeros achieved at each stage (initial LP solution, L1-norm solution, and each successive warm-started L0 iteration)

• error_code – 0 - success; 1 - the initial LP is unbounded/infeasible

• nb_warm_start – Number of warm-start (Theta L0) iterations performed

• z – n x 1 sparsest solution vector found

findMinimalSetOfRxns(model)

This function finds the minimal set of reactions subject to a LP objective function \(min ||x||_0\) \(min c'x\) s.t. \(Sx = b\) \(lb <= x <= ub\)

USAGE:

[result_tab, sol, lprxns, l1rxns, l0rxns] = findMinimalSetOfRxns (model)

INPUT:

model – COBRA model structure with fields:

• .c - Objective coefficients

• .S - Stoichiometric matrix

• .b - Right hand side of S*x = b

• .lb - Lower bound vector

• .ub - Upper bound vector

OUTPUTS:

• result_tab – number of reactions obtained for each condition

• sol – x - solution vector

• lprxns – rxns indices for LP solution

• l1rxns – rxns indices for L1 solution

• l0rxns – rxns indices for L0 solution

main_norm0

Code matlab