最优化与控制
We analyze Nesterov's accelerated gradient descent (NAGD) for Nash equilibrium seeking in $N$-player quadratic games. While the continuous-time NAGD dynamics -- the Su--Boyd--Cand\`{e}s ODE -- are well understood for convex optimization,…
Trajectory design in cislunar space under a High-Fidelity Ephemeris Model (HFEM) is pursued through a nonlinear optimization perspective anchored on the transition of solutions from lower fidelity models, namely the Circular Restricted…
Fish migration is a mass movement that affects the hydrosphere and ecosystems. While it occurs on multiple temporal scales, including daily and intraday fluctuations, the latter remains less studied. In this study, for a stochastic…
Designing satellite constellation systems involves complex multidisciplinary optimization in which coverage serves as a primary driver of overall system cost and performance. Among the various design considerations, constellation…
We discuss optimization problems over convex cones in which membership is difficult to verify directly. In the standard theory of duality, vectors in the dual cone $K^*$ are associated with separating hyperplanes and interpreted as…
When are two algorithms the same? How can we be sure a recently proposed algorithm is novel, and not a minor variation on an existing method? In this paper, we present a framework for reasoning about equivalence between a broad class of…
Sequential quadratic programming and sequential convex programming efficiently solve nonlinear programs (NLPs) by linearizing inner nonlinearities while preserving the outer convex structure. This paper introduces a sequential mixed-integer…
We study the linear-quadratic optimal control problem for infinite-dimensional dissipative systems with possibly indefinite cost functional. Under the assumption that a storage function exists, we show that this indefinite optimal control…
The Abelian sandpile model serves as a canonical example of self-organized criticality. This critical behavior manifests itself through large cascading events triggered by small perturbations. Such large-scale events, known as avalanches,…
The cyclic hoist scheduling problem originates in electroplating lines, where a single or multiple hoists transport parts between processing tanks subject to technological constraints. The objective is typically to determine a cyclic…
Landing methods have recently emerged in Riemannian matrix optimization as efficient schemes for handling nonlinear equality constraints without resorting to costly retractions. These methods decompose the search direction into tangent and…
A classical proposal to derive weights from a pairwise comparison matrix is the right eigenvector. The literature has identified some potential weaknesses of this method in previous decades. This chapter discusses five of these issues.…
For simultaneous independent events with finitely many outcomes, consider the expected-utility problem with nonnegative wagers and an endogenous cash position. We prove a short support theorem for a broad class of strictly increasing…
Reconstruction in limited-angle digital breast tomosynthesis (DBT) suffers from slow convergence of low spatial-frequency components when using weighted data-fidelity terms within primal-dual optimization. We introduce a two-channel…
We formulate and solve a discrete-time linear-quadratic regulation (LQR) problem in a finite horizon that penalizes temporal variability and stochastic variability of the state trajectory. Our approach enables the user to strike a balance…
We provide quantitative convergence results for continuous-time dynamical systems in metric spaces that satisfy a continuous-time analog of quasi-Fej\'er monotonicity. More precisely, we provide a (strong) convergence result for such…
We propose a globally convergent trust-region bundle method for minimizing lower-$C^2$ functions using higher-order cutting-plane models. Under certain growth assumptions on the objective around its minimum, the method is able to compute…
A cutting-plane model for a nonsmooth function is the maximum of several first-order expansions centered at different points. Using such a model in a bundle method leads to linear convergence (of serious steps) to a minimum. In smooth…
We expand our novel computational method for unit commitment (UC) to include long-horizon planning. We introduce a fast novel algorithm to commit hydro-generators, provably accurately. We solve problems with thousands of generators at 5…
We propose a novel computational method for unit commitment UC, which does not require linearized approximation and provides several orders of magnitude performance improvement over current state-of-the-art. The performance improvement is…