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A gradient-based method for joint chance-constrained optimization with continuous distributions
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DOI：10.1080/10556788.2025.2581585.png)
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Abstract
En 中文
The input parameters of an optimization problem are often affected by uncertainties. Chance constraints are one way to model stochastic uncertainties in the constraints. Typically, solution algorithms for chance-constrained problems require convex functions or discrete distributions. Here, we go one step further and allow non-convexities and continuous distributions. We propose a gradient-based approach to approximately solve joint chance-constrained models. We approximate the original problem by smoothing indicator functions. The smoothed chance constraints are relaxed by penalizing their violation in the objective function. The approximation problem is solved with the Continuous Stochastic Gradient method that is an enhanced version of the stochastic gradient descent and has recently been introduced in the literature. We present a convergence theory for the smoothing and penalty approximations. Under very mild assumptions, our approach is applicable to a wide range of problems. We illustrate its computational efficiency on difficult practical problems in gas networks. The numerical experiments demonstrate that the approach quickly finds nearly feasible solutions for joint chance-constrained problems with non-convex constraint functions and continuous distributions, even for realistically-sized instances.
Keywords:
Joint chance constraints
continuous distributions
smoothing
penalization
Continuous Stochastic Gradient method
energy networks
Journal
O
IF:
1.4
Papers:
24
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0