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Traditional optimization procedures were mostly developed under the constraints of limited memory in computer hardware and based on the use of real variables. The most prominent example is the award winning simplex method of linear programming. It embodies the essence of point-to-point iteration based on local information of directions of feasible descent (for minimization problems). However, with the advance in inexpensive computer memory and the prevalence of combinatorial type of system optimization problems, emphasis in solution approaches begin to shifts towards set-to set iteration of narrowing down the search. In this talk we shall examine this developing paradigm for optimization and discuss progress in this field of research.