Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A chance constrained problem involves a set of scenario constraints from which a small subset can be violated. Existing works typically consider a mixed integer programming MIP formulation of this problem by introducing binary variables to indicate which constraint systems are to be satisfied or violated. A variety of cutting plane approaches for this MIP formulation have been developed.   consider a family of cuts for chance constrained problems in the original space rather than those in the extended space of the MIP reformulation. These cuts, known as quantile cuts, can be vied as a projection of the ll known family of mixing inequalities for the MIP reformulation, onto the original problem space.  show the following results regarding quantile cuts: i the closure of all quantile cuts is a polyhedral set; ii separation of quantile cuts is in general NP-hard; iii successive application of quantile cut closures achieves the convex hull of the chance constrained problem in the limit; and iv in the pure integer setting this convergence is finite.
['Weijun Xie', 'Shabbir Ahmed']
I am writing a research paper on a idea On the Quantile Cut Closure of Chance-Constrained Problems
[{"from": "human", "value": "I am writing a research paper on a idea On the Quantile Cut Closure of Chance-Constrained Problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A chance constrained problem involves a set of scenario constraints from which a small subset can be violated. Existing works typically consider a mixed integer programming MIP formulation of this problem by introducing binary variables to indicate which constraint systems are to be satisfied or violated. A variety of cutting plane approaches for this MIP formulation have been developed.   consider a family of cuts for chance constrained problems in the original space rather than those in the extended space of the MIP reformulation. These cuts, known as quantile cuts, can be vied as a projection of the ll known family of mixing inequalities for the MIP reformulation, onto the original problem space.  show the following results regarding quantile cuts: i the closure of all quantile cuts is a polyhedral set; ii separation of quantile cuts is in general NP-hard; iii successive application of quantile cut closures achieves the convex hull of the chance constrained problem in the limit; and iv in the pure integer setting this convergence is finite."}]