A Historical View of Nonlinear Programming: Traces and Emergence

The historical view we propose in this introductory chapter will point out some of the technical difficulties of mathematical problems related to nonlinear programming and some features of the economic and social context (also military) that favored its rootedness in the years of the Second World War and the years immediately following the war. We recall some of the main definitions and basic results of mathematical programming and shortly address the “prehistory” of nonlinear programming. The main part of the chapter deals with the first ideas and developments of linear programming, first in the USSR and then in the USA and with the fundamental researches ofW. Karush, Fritz John, H.W. Kuhn and A.W. Tucker which are analyzed and discussed with respect to their mathematical and historical features.