This paper outlines a generalized, systematic design approach to solution of the non-convex quadratic programming problem. It is based on a previous formulation of utility of a general system in terms of efficiency and robustness of the system. The approach is to introduce a robustness term of arbitrary magnitude into the design utility function. Mathematically, this makes the problem convex. From a design approach, it yields a more general solution allowing specialization to proceed by decreasing robustness (on an initially convex utility surface in the feasible design space) until the region of the overall optimum is approached. The approach is mathematically related to the Metropolis technique of simulated annealing but a more systematic (less random) solution process is used. It is analogous also to the heuristic technique of \textit{R. E. Burkard} and \textit{T. Boenninger} [Eur. J. Oper. Res. 13, 374-386 (1983; Zbl 0509.90058)]. These two previous techniques are the most effective so far reported for the quadratic programming problem. The robustness approach provides an underpinning for each and opens up further solution options. Applications include layout of buildings and other constructed facilities and information technology layout problems.