Formulation help

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nick wilson

2024年09月06日 23:43

I have a midsized stochastic program that's experience longer runtimes than I'd like. I'm simplifying some notation, but the crux of my problem is: I have a known entity, d, and nonnegative variables, x and l. I have some simple constraints x <=d and x<= l, and then x = min(l, d). The minimum is there to keep things consistent across scenarios in my model, so it's needed. In effect what it does is when x << d, it sets l = x. I was toying around with using a quadratic constraint to approximate this as follows: l <= x + 1/(d-x) or equivalently (l-x)(d-x) <= 1, so when x << d the constraint relaxes and allows l > x. Arguably, we could replace the 1 with an arbitrary constant for tuning. Unfortunately, this is nonconvex. I was wondering if your team might have a suggestion on something else to try.

関連

• Big-M
• Stochastic

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  Simranjit Kaur

  • Gurobi Staff

  2026年11月13日 01:20

  This post is more than two years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.
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  Riley Clement

  • Gurobi Staff

  2024年09月09日 04:08

  Hi Nick,

  Using a quadratic expression is likely a step in the wrong direction.  You could use Gurobi's "MIN" function - in gurobipy this is addGenConstrMin, or you could introduce a binary variable y and use the following set of constraints

  x <= l
  x <= d   # better as an upper bound, rather than constraint
  x >= d*y
  x >= l - y*l.ub

  where l.ub is an upper bound on l.

  Note that if your objective function naturally causes the x variable to want to be as large as possible then you will only need the first two of these constraints.

  - Riley

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