In Shallit’s problem (SIAM Review, 1994), it was proposed to justify a two-term asymptotics of the minimum rational function $$n$$ variables defined as sum special form whose number terms is order $$n^2$$ $$n\to\infty$$ . Of particular interest second term this (“Shallit’s constant”). The solution published in SIAM Review presented an iteration algorithm for calculating constant, which conta...

In this note, we generalize the affine rank minimization problem and the vector cardinality minimization problem and show that the resulting generalized problem can be solved by solving a sequence of continuous concave minimization problems. In the case of the vector cardinality minimization problem, we show that it can be solved by solving the continuous concave minimization problem.