An analog approach alternative to the Hopfield method is presented for solving constrained combinatorial optimization problems. In this new method, a saddle point of a Lagrangian function is searched using a constrained dynamical system with the aid of an appropriate transformation of variables. This method always gives feasible solutions in contrast to the Hopfield scheme which often outputs infeasible solutions. The convergence of the method is proved theoretically and some effective schemes are recommended for eliminating some variables for the case we resort to numerical simulation. An analog electronic circuit is devised which implements this method. This circuit requires fewer wirings than the Hopfield networks. Furthermore this circuit dissipates little electrical power owing to subthreshold operation of MOS transistors. An annealing process, if desired, can be performed easily by gradual increase in resistance of linear resistors in contrast to the Hopfield circuit which requires the variation in the gain of amplifiers. The objective function called an energy is ensured theoretically to decrease throughout the annealing process.