Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Optimization-based bound tightening (OBBT) is a domain reduction technique commonly used in nonconvex mixed-integer nonlinear programming that solves a sequence of auxiliary linear programs. Each variable is minimized and maximized to obtain the tightest bounds valid for a global linear relaxation.  shows how the dual solutions of the auxiliary linear programs can be used to learn what  call Lagrangian variable bound constraints.  These are linear inequalities that explain OBBT's domain reductions in terms of the bounds on other variables and the objective value of the incumbent solution. Within a spatial branch-and-bound algorithm, they can be learnt a priori (during OBBT at the root node) and propagated within the search tree at very low computational cost. Experiments with an implementation inside the MINLP solver SCIP show that this reduces the number of branch-and-bound nodes and speeds up solution times.
['Ambros M. Gleixner', 'Stefan Weltge']
I am writing a research paper on a idea Learning and Propagating Lagrangian Variable Bounds for Mixed-Integer Nonlinear Programming
[{"from": "human", "value": "I am writing a research paper on a idea Learning and Propagating Lagrangian Variable Bounds for Mixed-Integer Nonlinear Programming"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Optimization-based bound tightening (OBBT) is a domain reduction technique commonly used in nonconvex mixed-integer nonlinear programming that solves a sequence of auxiliary linear programs. Each variable is minimized and maximized to obtain the tightest bounds valid for a global linear relaxation.  shows how the dual solutions of the auxiliary linear programs can be used to learn what  call Lagrangian variable bound constraints.  These are linear inequalities that explain OBBT's domain reductions in terms of the bounds on other variables and the objective value of the incumbent solution. Within a spatial branch-and-bound algorithm, they can be learnt a priori (during OBBT at the root node) and propagated within the search tree at very low computational cost. Experiments with an implementation inside the MINLP solver SCIP show that this reduces the number of branch-and-bound nodes and speeds up solution times."}]