Abstract
This chapter discusses the piecewise linear approximation method. Polishchuk developed a method for approximating the non-inferior set in convex programming problems with two objective functions. In this a posteriori method, preference information comes into play only after a piecewise approximation has been made of the problem's non-inferior set. The method bears striking similarities to the non-inferior set estimation (NISE) method developed by American researchers Cohon, Church, and Sheer at about the same time. Like the NISE method, Polishchuk's procedure not only attempts to give a piecewise linear approximation of the non-inferior set in problems with two objective functions but also includes a metric that is used to gauge the maximum possible error in the approximation at each step in the iteration process. Whereas the NISE method was developed specifically for linear programming problems, Polishchuk's method is applicable to the broader class of convex programming problems.
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