最优化与控制

Consensus planning is a method for coordinating decision making across complex systems and organizations, including complex supply chain optimization pipelines. It arises when large interdependent distributed agents (systems) share common…

While Variational Inequality (VI) is a well-established mathematical framework that subsumes Nash equilibrium and saddle-point problems, less is known about its extension, Quasi-Variational Inequalities (QVI). QVI allows for cases where the…

Safety is closely related to set invariance for dynamical systems. However, synthesizing a safe invariant set and at the same time synthesizing the associated safe controller still remains challenging. In this note we introduce a simple…

Stochastic gradient descent is one of the most common iterative algorithms used in machine learning and its convergence analysis is a rich area of research. Understanding its convergence properties can help inform what modifications of it…

We consider some important computational aspects of the long-step path-following algorithm developed in our previous work and show that a broad class of complicated optimization problems arising in quantum information theory can be solved…

The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…

We study linear policy approximations for the risk-conscious operation of an industrial energy system with uncertain wind power, significant and variable electricity demand, and high thermal output, as found in a modern foundry. The system…

This paper presents a new interpretation of the Lyapunov and Riccati equations from the perspective of positive system theory. We show it is possible to construct positive systems related to these equations, and then certain conclusions --…

In this paper, we introduce the G\"uler-type acceleration technique and utilize it to propose three acceleration algorithms: the G\"uler-type accelerated proximal gradient method (GPGM), the G\"uler-type accelerated linearized augmented…

In this paper, we consider the multiple probabilistic covering location problem (MPCLP), which attempts to open a fixed number of facilities to maximize the total covered customer demand under a joint probabilistic coverage setting. We…

This paper investigates the robustness of stochastic optimal control for controlled regime switching diffusions. We consider systems driven by both continuous fluctuations and discrete regime changes, allowing for model misspecification in…

We study the Carath\'eodory number of homogeneous convex cones via their spectrahedral representations. A characterization of homogeneous convex cones whose ranks match their Carath\'eodory numbers is given. This characterization is then…

This paper studies infinite horizon linear quadratic (LQ) mean field problems with common noise and regime switching, covering both control and game formulations. To establish a theoretical foundation for the LQ framework, we first analyze…

Contextual stochastic optimization is an advanced methodology to model uncertainty in the presence of contextual information during decision planning processes. Although classical methodologies focus on minimizing the expectation of a…

We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise…

This paper investigates noise-robust phase retrieval by enhancing the prDeep architecture with difference of convex functions (DC) and DnCNN-based denoising regularization. This research introduces two novel algorithms, prDeep-DC and…

Penalty-based methods have become popular for solving bilevel optimization (BLO) problems, thanks to their effective first-order nature. However, they often require inner-loop iterations to solve the lower-level (LL) problem and small…

The paper considers the problems of optimal vaccination control in the classical SIR model under constraints on the resource capabilities of the insurance medical system, in particular under constraints on the possible absolute rate of…

We analyze a zeroth-order particle algorithm for the global optimization of a non-convex function, focusing on a variant of Consensus-Based Optimization (CBO) with small but fixed noise intensity. Unlike most previous studies restricted to…

We consider the use of pricing as a regulatory mechanism when an unknown number of autonomous agents compete for access to a shared resource (possibly limited in volume or capacity). In standard dynamic pricing control systems, an…