Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the Scenario Convex Program (SCP) for two classes of optimization problems that are not tractable in general: Robust Convex Programs (RCPs) and Chance-Constrained Programs (CCPs).  establish a probabilistic bridge from the optimal value of SCP to the optimal values of RCP and CCP in which the uncertainty takes values in a general, possibly infinite dimensional, metric space.  then extend our results to a certain class of non-convex problems that includes, for example, binary decision variables. In the process,  also settle a measurability issue for a general class of scenario programs, which to date has been addressed by an assumption. Finally,  demonstrate the applicability of our results on a benchmark problem and a problem in fault detection and isolation.
['Peyman Mohajerin Esfahani', 'Tobias Sutter', 'John Lygeros']
I am writing a research paper on a idea Performance Bounds for the Scenario Approach and an Extension to a Class of Non-convex Programs
[{"from": "human", "value": "I am writing a research paper on a idea Performance Bounds for the Scenario Approach and an Extension to a Class of Non-convex Programs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the Scenario Convex Program (SCP) for two classes of optimization problems that are not tractable in general: Robust Convex Programs (RCPs) and Chance-Constrained Programs (CCPs).  establish a probabilistic bridge from the optimal value of SCP to the optimal values of RCP and CCP in which the uncertainty takes values in a general, possibly infinite dimensional, metric space.  then extend our results to a certain class of non-convex problems that includes, for example, binary decision variables. In the process,  also settle a measurability issue for a general class of scenario programs, which to date has been addressed by an assumption. Finally,  demonstrate the applicability of our results on a benchmark problem and a problem in fault detection and isolation."}]