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The subject of this paper is a classification and discussion of algorithms for solution of nonlinear pure integer programming problems. The survey is organized by characterizing the mathematical form of the nonlinear optimization problems addressed by the various algorithms. If any method can be used without changes to solve mixed integer nonlinear programming problems that fact is mentioned in the description of the algorithm. However algorithms which must be applied only to mixed integer problems are not surveyed.programming: integer nonlinear algorithm

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This paper presents an application of a method for finding the global solution to a problem in integers with a separable objective function of a very general form. This report shows that there is a relationship between an integer problem with a separable nonlinear objective function and many constraints and a series of nonlinear problems with only a single constraint, each of which can be solved sequentially using dynamic programming. The first solution to any of the individual smaller problems that satisfies the original constraints in addition, will be the optimal solution to the multiply-constrained problem.

An algorithm is presented to gain postoptimality data about the family of nonlinear pure integer programming problems in which the objective function and constraints remain the same except for changes in the right-hand side of the constraints. I t is possible 10 solve such families of problems simultaneously to give a global optimum for each problem in the family. with additional problems solved in under 2 CPU seconds. This represents a small fraction of the time necessary to solve each problem individually.