A derivative algorithm for inexact quadratic program – application to environmental decision-making under uncertainty

Inexact quadratic programming (IQP) is an extension of conventional quadratic programming for handling both nonlinearities in cost objectives and uncertainties with modeling parameters. It has been a useful tool for environmental systems analysis. However, inefficiency in its solution method has existed, leading to difficulties in its practical application. In this study, a derivative algorithm (DAM) is proposed for solving the IQP. It improves upon the existing method through provision of a quantitative expression for uncertain relationships between the quadratic objective function and the decision variables. The DAM requires much lower computational efforts than the existing algorithm, which is especially meaningful for the IQP's application to large-scale problems. The developed DAM is applied to a hypothetical problem of municipal solid waste management and planning. Detailed solution steps are provided to clearly demonstrate the method's advantages.