Related papers: Safe Zeroth-Order Optimization Using Linear Progra…
Partitioning for load balancing is a crucial first step to parallelize any type of computation. In this work, we propose SGORP, a new spatial partitioning method based on Subgradient Optimization, to solve the $d$-dimensional Rectilinear…
In this paper, we study zeroth-order algorithms for nonconvex minimax problems with coupled linear constraints under the deterministic and stochastic settings, which have attracted wide attention in machine learning, signal processing and…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
Language Models (LLMs) are often quantized to lower precision to reduce the memory cost and latency in inference. However, quantization often degrades model performance, thus fine-tuning is required for various down-stream tasks.…
A sparse linear programming (SLP) problem is a linear programming problem equipped with a sparsity (or cardinality) constraint, which is nonconvex and discontinuous theoretically and generally NP-hard computationally due to the…
Zeroth-order (ZO) optimization has become a popular technique for solving machine learning (ML) problems when first-order (FO) information is difficult or impossible to obtain. However, the scalability of ZO optimization remains an open…
This note uses the Total Least-Squares (TLS) line-fitting problem as a canvas to explore some modern optimization tools. The contribution is meant to be tutorial in nature. The TLS problem has a lot of mathematical similarities to important…
Various first order approaches have been proposed in the literature to solve Linear Programming (LP) problems, recently leading to practically efficient solvers for large-scale LPs. From a theoretical perspective, linear convergence rates…
This paper presents an offline motion planner for linear cyber-physical systems that satisfy a continuous-time Signal Temporal Logic (STL) specification, in which controls are applied in a Zeroth-order Hold (ZOH) manner. The motion planning…
This paper investigates numerical methods for solving stochastic linear quadratic (SLQ) optimal control problems governed by stochastic partial differential equations (SPDEs). Two distinct approaches, the open-loop and closed-loop ones, are…
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…
Recent road trials have shown that guaranteeing the safety of driving decisions is essential for the wider adoption of autonomous vehicle technology. One promising direction is to pose safety requirements as planning constraints in…
Tools from control and dynamical systems have proven valuable for analyzing and developing optimization methods. In this paper, we establish rigorous theoretical foundations for using feedback linearization (FL) -- a well-established…
This paper proposes low-complexity algorithms for finding approximate second-order stationary points (SOSPs) of problems with smooth non-convex objective and linear constraints. While finding (approximate) SOSPs is computationally…
We present two first-order primal-dual algorithms for solving saddle point formulations of linear programs, namely FWLP (Frank-Wolfe Linear Programming) and FWLP-P. The former iteratively applies the Frank-Wolfe algorithm to both the primal…
In the development of industrial digital twins, the optimization problem of technological and business processes often arises. In many cases, this problem can be reduced to a large-scale linear programming (LP) problem. The article is…
Recent advances in derivative-free optimization allow efficient approximation of the global-optimal solutions of sophisticated functions, such as functions with many local optima, non-differentiable and non-continuous functions. This…
Zeroth-order or derivative-free optimization (MeZO) is an attractive strategy for finetuning large language models (LLMs) because it eliminates the memory overhead of backpropagation. However, it converges slowly due to the inherent curse…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
This paper proposes a learning-based approach to accelerate the interior-point method (IPM) for solving optimal power flow (OPF) problems by learning the structure of the IPM central path from its early stable iterations. Unlike traditional…