最优化与控制
A standard assumption in multistage stochastic programming is that decisions are made after observing the uncertainty from the prior stage. The resulting solutions can be difficult to implement in practice, as they leave practitioners…
Offline policy learning aims to use historical data to learn an optimal personalized decision rule. In the standard estimate-then-optimize framework, reweighting-based methods (e.g., inverse propensity weighting or doubly robust estimators)…
This paper investigates the output feedback stabilization of parabolic equation with Lipschitz nonlinearity over general multidimensional domain using spectral geometry theories. First, a novel nonlinear observer is designed, and the error…
We propose a high-order version of the augmented Lagrangian method for solving convex optimization problems with linear constraints, which achieves arbitrarily fast -- and even superlinear -- convergence rates. First, we analyze the…
Two algorithms are proposed, analyzed, and tested for solving continuous optimization problems with nonlinear equality constraints. Each is an extension of a stochastic momentum-based method from the unconstrained setting to the setting of…
Generalized Disjunctive Programming (GDP) provides a powerful framework for combining algebraic constraints with logical disjunctions. To solve these problems, mixed-integer reformulations are required, but traditional reformulation…
This paper presents a new extension of the classical Heron problem, termed the generalized $(k,m)$-Heron problem, which seeks an optimal configuration among $k$ feasible and $m$ target non-empty closed convex sets in $\mathbb{R}^n$. The…
Many years ago John Tyrell a lecturer at King's college London challenged his Ph.D. students with the following puzzle: show that there is a unique triangle of minimal perimeter with exactly one vertex to lie on one of three given lines,…
We introduce a numerically stable reformulation of controllability scoring based on a scaled controllability Gramian, which remains reliably computable even for unstable systems. The resulting optimization problems define dynamics-aware…
Purpose: The model allocates the system components orders to the suppliers to minimize the parts price and the system construction delay penalties and maximize the system availability during its use. It considers the quantity-based discount…
We study SOS properties of biquadratic forms. For the class of partially symmetric biquadratic forms, we establish necessary and sufficient conditions for positive semi-definiteness and prove that every PSD partially symmetric biquadratic…
This document, intended for computer science teachers, describes a case study that puts into practice a questioning of ethical, societal and environmental issues when designing or implementing a decision support system. This study is based…
The Nesterov accelerated gradient method, introduced in 1983, has been a cornerstone of optimization theory and practice. Yet the question of its point convergence had remained open. In this work, we resolve this longstanding open problem…
We consider a novel approach for the enhancement of fluid mixing via pure stirring strategies building upon the Least Action Principle (LAP) for incompressible flows. The LAP is formally analogous to the Benamou--Brenier formulation of…
In this paper we design a novel class of online distributed optimization algorithms leveraging control theoretical techniques. We start by focusing on quadratic costs, and assuming to know an internal model of their variation. In this…
In 1996, Meshulam proved that every sequence generated by applying projections onto affine subspaces, drawn from a finite collection in Euclidean space, must be bounded. In this paper, we extend his result not only from affine subspaces to…
In this paper, we introduce two new types of barrier certificates that are based on multiple functions rather than a single one. A conventional barrier certificate for a stochastic dynamical system is a nonnegative real-valued function…
We prove a necessary optimality condition of Euler--Lagrange type for the calculus of variations with Omega derivatives, which turns out to be sufficient under jointly convexity of the Lagrangian.
We develop a quantitative contraction framework for Schrodinger and Sinkhorn bridges based on transportation-cost inequalities and Riccati matrix difference equations. Our approach combines logarithmic Sobolev and Talagrand-type…
We develop a Lyapunov-based analysis of Korpelevich's extragradient method and show that it achieves an $o(1/k)$ last-iterate convergence rate of the constructed Lyapunov function. This Lyapunov function simultaneously upper bounds several…