Related papers: Finite Horizon Optimization: Framework and Applica…
In this paper, we propose a Feasible Sequential Linear Programming (FSLP) algorithm applied to time-optimal control problems (TOCP) obtained through direct multiple shooting discretization. This method is motivated by TOCP with nonlinear…
We introduce a machine-learning framework to learn the hyperparameter sequence of first-order methods (e.g., the step sizes in gradient descent) to quickly solve parametric convex optimization problems. Our computational architecture…
Markov Decision Processes (MDPs) have been used to formulate many decision-making problems in science and engineering. The objective is to synthesize the best decision (action selection) policies to maximize expected rewards (or minimize…
We propose the first general and scalable framework to design certifiable algorithms for robust geometric perception in the presence of outliers. Our first contribution is to show that estimation using common robust costs, such as truncated…
First-order primal-dual methods are appealing for their low memory overhead, fast iterations, and effective parallelization. However, they are often slow at finding high accuracy solutions, which creates a barrier to their use in…
In this paper, we study multistage stochastic mixed-integer nonlinear programs (MS-MINLP). This general class of problems encompasses, as important special cases, multistage stochastic convex optimization with non-Lipschitzian value…
Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…
This note re-visits the rolling-horizon control approach to the problem of a Markov decision process (MDP) with infinite-horizon discounted expected reward criterion. Distinguished from the classical value-iteration approach, we develop an…
An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…
Topology optimization of frame structures under free-vibration eigenvalue constraints constitutes a challenging nonconvex polynomial optimization problem with disconnected feasible sets. In this article, we first formulate it as a…
Online linear programming (OLP) has gained significant attention from both researchers and practitioners due to its extensive applications, such as online auction, network revenue management, order fulfillment and advertising. Existing OLP…
In this work, solution of the finite horizon hybrid optimal control problem as the central element of the receding horizon optimal control (model predictive control) is investigated based on the indirect approach. The response of a hybrid…
Real-world experiments involve batched & delayed feedback, non-stationarity, multiple objectives & constraints, and (often some) personalization. Tailoring adaptive methods to address these challenges on a per-problem basis is infeasible,…
It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…
Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
This paper is devoted to the design of efficient primal-dual algorithm (PDA) for solving convex optimization problems with known saddle-point structure. We present a new PDA with larger acceptable range of parameters and correction, which…
We show that the effects of finite-precision arithmetic in forming and solving the linear system that arises at each iteration of primal-dual interior-point algorithms for nonlinear programming are benign, provided that the iterates satisfy…
In complex engineered systems, completing an objective is sometimes not enough. The system must be able to reach a set performance characteristic, such as an unmanned aerial vehicle flying from point A to point B, \textit{under 10 seconds}.…
This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint…