323. Efficient computation of convex hull prices with level and subgradient methods: a computational comparison of dual methods
Invited abstract in session WC-7: Optimization applications I, stream Optimization applications.
Wednesday, 10:05 - 11:20Room: M:I
Authors (first author is the speaker)
| 1. | Sofiane Tanji
|
| UCLouvain | |
| 2. | yassine kamri
|
| INMA, UCLouvain | |
| 3. | François Glineur
|
| ICTEAM/INMA & CORE, Université catholique de Louvain (UCLouvain) | |
| 4. | Mehdi Madani
|
| N-SIDE |
Abstract
Convex Hull (CH) Pricing, used on US electricity markets and raising interest in Europe, is a pricing rule designed to handle markets in the presence of non-convexities such as startup costs and minimum uptimes.
In such markets, the market operator makes side payments to generators to cover lost opportunity costs, and CH prices are those who minimize such side payments. These prices can also be obtained by solving a (partial) Lagrangian dual of the original mixed-integer program, where power balance constraints are dualized. Computing CH prices then amounts to minimizing a sum of nonsmooth convex objective functions, where each term depends only on a single generator. The subgradient of each of those terms can be obtained independently by solving smaller mixed-integer programs.
In this work, we benchmark a large panel of first-order methods to solve the above dual CH pricing problem. We test eight algorithms, namely the bundle level method and a proximal variant, subgradient methods with various stepsize strategies, two recent parameter-free methods and an accelerated gradient method combined with smoothing. We compare those methods on two representative sets of real-world medium-scale instances, and include a recently proposed purely primal column generation method for reference. Our numerical experiments show that the bundle proximal level method and two variants of the subgradient method perform most favorably compared to other methods recently proposed.
Keywords
- Optimization in industry, business and finance
- Convex and non-smooth optimization
- Analysis and engineering of optimization algorithms
Status: accepted
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