Implied constraints and LP duals of general nonlinear programming problems

Article Abstract:

A study was conducted to show the existence of a family of linear programming (LP) duals for general nonlinear programming problems. The general dual problem was formulated from implied constraints using a simple bounding method. The Lagrangian dual was then characterized as a special case for the general dual while LP duals supported a powerful computation device determined by strict conditions. Finally, a novel concept of local duality related to the idea of local optimality was developed.

Operations Research, Research, Linear programming

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Optimal partitions for shop floor control in semiconductor wafer fabrication

Article Abstract:

An optimal scheduling method for semiconductor wafer fabrication is developed. Optimal partitioning of the steps in the manufacturing process is determined by finding the minimum sum of squares of deviations of partition sizes from a target size. The optimal partition can be found by expressing the problem as a dynamic program. An iterative heuristic is proposed to yield approximate solutions to the problem.

Usage, Scheduling (Management), Manufacturing processes, Manufacturing, Semiconductor wafers, Dynamic programming, Partitions (Mathematics)

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Implied constraints and an alternate unified development of nonlinear programming theory

Article Abstract:

A unified theory of nonlinear programming from the perspective of implied constraints is presented. Implied constraints characterize optimality and duality for both constrained and unconstrained problems. A weaker The approach's algorithmic potential is exhibited by showing that the Simplex method systematically works toward implying the objective from the given constraints of the problem.

Analysis, Mathematical optimization, Optimization theory, Duality theory (Mathematics), Simplex method, Simplexes (Mathematics)

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