Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The values of optimal solutions to the various dual relaxations of integer programs can be vied as functions of their multipliers. Successful search procedures have been developed for optimal lagrangian (piecewise linear concave) and surrogate (quasi-concave) multipliers. This note demonstrates that the composite and multiple surrogate dual functions lack quasi-concavity and may possess “false optima.” For the composite dual, complementary and alternate optimization over lagrangian and surrogate multipliers are shown to be nonoptimal techniques. Hover, some promising computational results, based on closing part of the gap beten the surrogate dual and the primal, are reported for the alternating approach.
['Mark H. Karwan', 'Ronald L. Rardin']
I am writing a research paper on a idea Technical Note—Searchability of the Composite and Multiple Surrogate Dual Functions
[{"from": "human", "value": "I am writing a research paper on a idea Technical Note\u2014Searchability of the Composite and Multiple Surrogate Dual Functions"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The values of optimal solutions to the various dual relaxations of integer programs can be vied as functions of their multipliers. Successful search procedures have been developed for optimal lagrangian (piecewise linear concave) and surrogate (quasi-concave) multipliers. This note demonstrates that the composite and multiple surrogate dual functions lack quasi-concavity and may possess \u201cfalse optima.\u201d For the composite dual, complementary and alternate optimization over lagrangian and surrogate multipliers are shown to be nonoptimal techniques. Hover, some promising computational results, based on closing part of the gap beten the surrogate dual and the primal, are reported for the alternating approach."}]