An industrial application of mathematical programming is presented. The objective is to propose a tool for computer aided design of compact plate fin heat exchangers. A proprietary sizing procedure, COLETH, is used to initialize the optimization problem and to evaluate the objective function and the constraints during the optimization problem resolution. The main features of COLETH are presented. The partial infeasible path strategy is discussed: at each optimization step, duty requirements are satisfied, but pressure drop constraints are not. Intermediate information can be used and the cpu time is quite low. A non linear programming optimization problem is formulated. Then the problem is solved using a reduced Hessien Successive Quadratic Programming algorithm, which can take advantage of the system sparcity. Other features of this algorithm are discussed. Three test problems are presented and the program abilities are illustrated.