NONCONVEX LINEAR PROGRAMMING.
CASE WESTERN RESERVE UNIV CLEVELAND OHIO DEPT OF OPERATIONS RESEARCH
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An algorithm for solving the nonconvex linear programming problem Maximize z cx, Subject to A sub ix or b sub i, 1 1,...,p for at least one i, x or 0 is given. The problem is viewed as one of n-dimensional geometry with the union of the p distinct solution sets a general nonconvex possibly disconnected polyhedral set. A continuous path in n-space is generated which passes from solution set to solution set as the optimum is sought. The core of the solution procedure is a linking linear program which is a efficient, highly flexible substitute for Phase I of the simplex method. Given an arbitrary linear programming problem in n decision variables and having m constraints, the linking linear program solution approach can conceivably produce an optimum basic feasible solution with little more computational effort than minimum n,m1 simplex pivot operations. Author
- Operations Research