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As in other estimation scenarios, likelihood based estimation in the normal mixture set-up is highly non-robust against model misspecification and presence of outliers (apart from being an ill-posed optimization problem). A robust…
This work develops an LLM-based optimization framework ensuring strict constraint satisfaction in network optimization. While LLMs possess contextual reasoning capabilities, existing approaches often fail to enforce constraints, causing…
Model Predictive Control (MPC) is a successful control methodology, which is applied to increasingly complex systems. However, real-time feasibility of MPC can be challenging for complex systems, certainly when an (extremely) large number…
This paper proposes a Clustered Unit Commitment (CUC) formulation to accurately model flexibility requirements such as ramping, reserve, and startup/shutdown constraints. The CUC is commonly applied in large and long-term planning models to…
In this note, we provide an overarching analysis of primal-dual dynamics associated to linear equality-constrained optimization problems using contraction analysis. For the well-known standard version of the problem: we establish…
Online decision making under uncertainty in partially observable domains, also known as Belief Space Planning, is a fundamental problem in robotics and Artificial Intelligence. Due to an abundance of plausible future unravelings,…
This paper studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus…
The problem of ensuring constraints satisfaction on the output of machine learning models is critical for many applications, especially in safety-critical domains. Modern approaches rely on penalty-based methods at training time, which do…
When considering an unconstrained minimization problem, a standard approach is to solve the optimality system with a Newton method possibly preconditioned by, e.g., nonlinear elimination. In this contribution, we argue that nonlinear…
Enforcing constraint satisfaction in neural network outputs is critical for safety, reliability, and physical fidelity in many control and decision-making applications. While soft-constrained methods penalize constraint violations during…
Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…
Accurately segmenting a citation string into fields for authors, titles, etc. is a challenging task because the output typically obeys various global constraints. Previous work has shown that modeling soft constraints, where the model is…
The instantaneous power generation from a hydroelectric turbine is proportional to the product of head difference and turbine flow. The equation relating power to hydraulic variables is therefore nonlinear. Hence, optimization problems…
Many problems in power systems involve optimizing a certain objective function subject to power flow equations and engineering constraints. A long-standing challenge in solving them is the nonconvexity of their feasible sets. In this paper,…
The problem of achieving a good trade-off in Stochastic Model Predictive Control between the competing goals of improving the average performance and reducing conservativeness, while still guaranteeing recursive feasibility and low…
Efficient methods for large-scale security constrained unit commitment (SCUC) problems have long been an important research topic and a challenge especially in market clearing computation. For large-scale SCUC, the Lagrangian relaxation…
Maintaining instantaneous balance between electricity supply and demand is critical for reliability and grid instability. System operators achieve this through solving the task of Unit Commitment (UC),ca high dimensional large-scale…
Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…
Linear tree constraints were introduced by Hofmann and Rodriguez in the context of amortized resource analysis for object oriented programs. More precisely, they gave a reduction from inference of resource types to constraint solving. Thus,…
Sparse optimization problems are ubiquitous in many fields such as statistics, signal/image processing and machine learning. This has led to the birth of many iterative algorithms to solve them. A powerful strategy to boost the performance…