Session: Advanced Computational Solver 2
Chair: Jingyi Wang
Cluster: Computational Software
Talk 1: Implicit Scenario Reduction for Superquantile-Constrained Optimization: Applications to Energy Systems
Speaker: Jake Roth
Abstract: We discuss an efficient and scalable second-order solver for solving large-scale optimization problems with superquantile (aka conditional value at risk) constraints based on the augmented Lagrangian and semismooth Newton method framework. Unlike empirical risk models, superquantile models have non-separable constraints that make typical first-order algorithms difficult to scale. In contrast, our computational approach scales well in terms of the number of training data due to an implicit first- and second-order sparsity associated with the superquantile operator. In particular, only a fraction of the set of scenarios contributes second-order information, resulting in computations that can be performed in a reduced space. When evaluating the risk of each scenario is expensive, the relative cost of second-order information is diminished. Our solver is expected to help control the risk of adverse events for safety-critical applications in the power grid.
Talk 2: Exponential cone optimization with COPT
Speaker: Joachim Dahl
Abstract: Recently there has been increasing interest in conic optimization over non-symmetric cones. One important example is the exponential cone, which has recently been implemented in leading commercial solvers including COPT. In this talk we give an overview of the algorithm implemented in COPT and present numerical results showing the advantage and feasibility of embedding conic representable sets involving exponentials into a conic algorithm.
Talk 3: Randomized Algorithms for Bayesian Inversion and Data Acquisition in Predictive Digital Twins
Speaker: Vishwas Rao
Abstract: A digital twin couples computational models with a physical counterpart to create a system that is dynamically updated through bidirectional data flows as conditions change. Data Assimilation and Optimal Experimental Design (OED) provide a systematic means of updating the computational model and acquiring information as the physical system evolves. This talk will describe scalable preconditioners and solvers for Bayesian inversion using different randomization techniques. The proposed techniques are amenable to parallelization and drastically reduce the required number of model evaluations. We also develop theoretical guarantees on the condition number. Additionally, the talk will describe connections between OED for Bayesian linear inverse problems and the column subset selection problem (CSSP) in matrix approximation and derive bounds, both lower and upper, for the D-optimality criterion via CSSP for the independent and colored noise cases. We demonstrate the performance and effectiveness of our methodology on a variety of test problems such as Burgers and quasi-geostrophic equations
