4 présentations

• 
  08h30 - 08h52

  Enhanced Lagrangian Cuts for Stochastic Mixed-Integer Programming

  • Haoxiang Yang, prés., The Chinese University of Hong Kong, Shenzhen
  • Hanbin Yang, The Chinese University of Hong Kong, Shenzhen

  This work proposes a globally converging cutting-plane algorithm for solving stochastic mixed-integer programs (SMIP) with general mixed-integer state variables. We show that Lagrangian cuts can approximate the convex envelope of the value function. To approximate the nonconvex value function to exactness, we need to iteratively add binary state variables and generate Lagrangian cuts on the lifted state space. We demonstrate that this lift-and-cut procedure converges to the global optimum with probability one. However, we show that vanilla Lagrangian cuts can be steep and lead to a poor lower approximation. We propose enhanced Lagrangian cuts, which strengthen the vanilla Lagrangian cut and yield good geometric properties. Extensive computational experiments on the generation expansion planning and security-constrained unit commitment problem demonstrate the effectiveness of our proposed methodology in solving large-scale, multistage stochastic mixed-integer optimization problems.

• 
  08h52 - 09h14

  Risk-Aware Security-Constrained Unit Commitment: Taming the Curse of Real-Time Volatility and Consumer Exposure

  • Daniel Bienstock, Columbia University
  • Yury Dvorkin, Johns Hopkins University
  • Cheng Guo, prés., Clemson University
  • Robert Mieth, Rutgers University
  • Jiayi Wang, Stanford University

  We propose an enhancement to wholesale electricity markets to contain the exposure of consumers to increasingly large and volatile consumer payments arising as a byproduct of volatile real-time net loads and prices, both compared to day-ahead cleared values. We incorporate a trade-off, motivated by portfolio optimization methods, between standard day-ahead payments and a robust estimate of such excess payments into the day-ahead computation and specifically seek to account for volatility in real-time net loads and renewable generation. Our model features a data-driven uncertainty set based on principal component analysis, which accommodates both load and wind production volatility and captures locational correlation of uncertain data. To solve the model more efficiently, we develop a decomposition algorithm that can handle nonconvex subproblems. Our extensive experiments on a realistic NYISO data set show that the risk-aware model protects the consumers from potential high costs caused by adverse circumstances.

• 
  09h14 - 09h36

  Reduced Sample Complexity in Scenario-Based Chance-Constrained Optimization via Constraint Scaling

  • Jaeseok Choi, prés., Pennsylvania State University
  • Anand Deo, Indian Institute of Management Bangalore
  • Constantino Lagoa, Pennsylvania State University
  • Anirudh Subramanyam, Pennsylvania State University

  The scenario approach, which replaces chance constraints with deterministic constraints based on random samples, is widely used for chance-constrained optimization due to its ability to preserve model structure. However, this method becomes computationally intractable for safety-critical applications with extreme events, as it requires an impractically large number of samples. To address this challenge, we propose a novel constraint scaling technique based on large deviation principles. Our approach significantly improves computational efficiency while maintaining feasibility compared to the standard scenario method. We validate our theoretical findings through numerical experiments on robust control problems.

• 
  09h36 - 09h58

  A Sequential Quadratic Programming Approach for Stochastic Optimization Problems with Stochastic Equality Constraints.

  • Haoming Shen, prés., University of Arkansas
  • Yang Zeng, Arizona State University
  • Baoyu Zhou, Arizona State University

  We propose a sequential quadratic programming approach for solving general smooth nonlinear stochastic optimization problems with stochastic equality constraints. The algorithm incorporates an adaptive step size strategy and only relies on crude estimates of the objective and constraints. We establish its asymptotic and non-asymptotic convergence guarantees under mild assumptions. Furthermore, numerical experiments on standard test cases demonstrate the method's efficiency and effectiveness.