We present an optimization-based inference scheme to unravel the functional interaction structure of biomolecular components within a cell. The regulatory network of a cell is inferred from the data obtained by perturbation of adjustable parameters or initial concentrations of specific components. It turns out that the identification procedure leads to a convex optimization problem with regularization as we have to achieve the sparsity of a network and also reflect any a priori information on the network structure. Since the convex optimization has been well studied for a long time, a variety of efficient algorithms were developed and many numerical solvers are freely available. In order to estimate time derivatives from discrete-time samples, a cubic spline fitting is incorporated into the proposed optimization procedure. Throughout simulation studies on several examples, it is shown that the proposed convex optimization scheme can effectively uncover the functional interaction structure of a biomolecular regulatory network with reasonable accuracy.