arXiv subjects

Jinda Yang

Publications and source records attributed to Jinda Yang.

3 recordsLinked to original sources

arXiv2026

Faster Stochastic ADMM for Nonsmooth Composite Convex Optimization in Hilbert Space

In this paper, a stochastic alternating direction method of multipliers (ADMM) is proposed for a class of nonsmooth composite and stochastic convex optimization problems in Hilbert space, motivated by optimization problems constrained by partial differential equation (PDE) with random coefficients. We prove the strong convergence of the proposed ADMM algorithm in the strongly convex case, and show the faster nonergodic convergence rates in terms of functional values and feasibility violation for both strongly convex and general convex cases. We demonstrate the application of the proposed method to solve certain model problems, along with its associated probability bound of large deviation. Some preliminary numerical results illustrate the efficiency of our method.

math.OC↗

arXiv2026

An Inexact Alternating Direction Method of Multipliers for Constrained Parabolic Optimal Distributed Control Problems

Solving parabolic optimal control problems can be inherently challenging in the field of science and engineering, especially with constraints on the nonsmooth distributed control. Motivated by the extensive applicability of the alternating direction method of multipliers, in this paper we develop a novel inexact algorithmic framework for parabolic optimal distributed control problems with control constraints. By decoupling the control constraint and possible nonsmooth objective from the optimal control problem, our aim is to efficiently solve the subproblem constrained by the parabolic state equation, for which computing a sufficiently accurate numerical solution can be prohibitively expensive. Given this high computational cost, we consider that it may not always be justifiable to compute a highly accurate solution of the subproblem at every iteration. Hence, we propose an inexact strategy for solving the parabolic equation constrained subproblem. Under mild and flexible conditions on the parameters, we prove global convergence and a linear convergence rate for the resulting algorithmic framework. In practice, our inexact algorithmic framework is easily implementable with applicable nested iterations. Numerical experiments are performed on different cases, and the results demonstrate the validity and trustworthy performance of the proposed methods.

math.OC↗

arXiv2025

LLMartini: Seamless and Interactive Leveraging of Multiple LLMs through Comparison and Composition

The growing diversity of large language models (LLMs) means users often need to compare and combine outputs from different models to obtain higher-quality or more comprehensive responses. However, switching between separate interfaces and manually integrating outputs is inherently inefficient, leading to a high cognitive burden and fragmented workflows. To address this, we present LLMartini, a novel interactive system that supports seamless comparison, selection, and intuitive cross-model composition tools. The system decomposes responses into semantically aligned segments based on task-specific criteria, automatically merges consensus content, and highlights model differences through color coding while preserving unique contributions. In a user study (N=18), LLMartini significantly outperformed conventional manual methods across all measured metrics, including task completion time, cognitive load, and user satisfaction. Our work highlights the importance of human-centered design in enhancing the efficiency and creativity of multi-LLM interactions and offers practical implications for leveraging the complementary strengths of various language models.

cs.HC↗