Bilevel optimization problems are known to be challenging to solve in practice. In particular, the feasible set of a bilevel problem is, in general, non-convex, even for linear bilevel problems. In this work, we aim to develop a better understanding of the feasible set of linear bilevel problems. Specifically, we develop means by which to … Read more
Robust optimization approaches compute solutions resilient to data uncertainty, represented by a given uncertainty set. Instead, the problem of computing the largest uncertainty set that a given solution can support was, so far, quite neglected and the only results refer to the single stage framework. For that setting, it was proved that this problem can … Read more
So far, robust optimization have focused on computing solutions resilient to data uncertainty, given an uncertainty set representing the possible realizations of this uncertainty. Here, instead, we are interested in answering the following question: once a solution of a problem is given, which is the largest uncertainty set that this solution can support? We address … Read more
We explore Maximum a Posteriori inference of Bayesian Hierarchical Models (BHMs) with intractable normalizers, which are increasingly prevalent in contemporary applications and pose computational challenges when combined with nonconvexity and nondifferentiability. To address these, we propose the Adaptive Importance Sampling-based Surrogation method, which efficiently handles nonconvexity and nondifferentiability while improving the sampling approximation of the … Read more
Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and imperfect observations, subject to additive noise, with the goal of minimizing a quadratic cost function for the state and control variables. In this work, … Read more
Sampling-based algorithms provide a practical approach to solving large-scale multistage stochastic programs. This chapter presents two alternative approaches to incorporating sampling within multistage stochastic linear programming algorithms. In the first approach, sampling is used to construct a sample average approximation (SAA) of the true multistage program. Subsequently, an optimization step is undertaken using deterministic decomposition … Read more
We study multistage stochastic optimization problems using sample average approximation (SAA) and model predictive control (MPC) as solution approaches. MPC is frequently employed when the size of the problem renders stochastic dynamic programming intractable, but it is unclear how this choice affects out-of-sample performance. To compare SAA and MPC out-of-sample, we formulate and solve an … Read more
The semismooth Newton method is a very efficient approach for computing a zero of a large class of nonsmooth equations. When the initial iterate is sufficiently close to a regular zero and the function is strongly semismooth, the generated sequence converges quadratically to that zero, while the iteration only requires to solve a linear system. … Read more
The complementarity between renewable generation profiles has been widely explored in the literature. Notwithstanding, the regulatory and economic frameworks for hybrid power plants add interesting challenges and opportunities for investors, regulators, and planners. Focusing on the Brazilian power market, this paper proposes a unified and isonomic firm energy certificate (FEC) calculation for non-controllable renewable generators, … Read more
\(\) A fundamental challenge in learning an unknown dynamical system is to reduce model uncertainty by making measurements while maintaining safety. In this work, we formulate a mathematical definition of what it means to safely learn a dynamical system by sequentially deciding where to initialize the next trajectory. In our framework, the state of the … Read more