The numerical solution of a Volterra integral equation of the first kind is a mildly ill-posed problem. To regularize it, the authors impose constraints based on the knowledge that the solution is nonincreasing and convex. Using the special structure of the constraints, they reduce the problem to an equivalent problem with a nonnegativity constraint, which can be solved more easily.

For the discretized problem, the authors compare this method to a method where only a nonnegativity constraint is imposed. Both a theoretical analysis and numerical experiments show that the authors’ method gives better results.

The idea of using linear inequality constraints rather than Tikhonov regularization is appealing, since in many cases it seems more natural to formulate a priori information about the solution in terms of nonnegativity and monotonicity than to select the value of a regularization parameter. The paper is well written and is a good contribution to the numerical solution of ill-posed problems.