arXiv subjects

Lixin Tang

Publications and source records attributed to Lixin Tang.

8 recordsLinked to original sources

arXiv2026

Primal-Dual Halpern-PAGE Algorithm for Constrained Stochastic Weakly Convex Optimization

We tackle the challenging problem of stochastic weakly convex optimization subject to mixed (equality and inequality) expected-value constraints. While optimal $\mathcal{O}(\epsilon^{-3})$ sample complexity algorithms exist for unconstrained weakly convex problems, dealing with complex functional constraints typically requires cumbersome multi-loop penalty or augmented Lagrangian methods, which suffer from high inner-loop complexity and sensitive parameter tuning. To bridge this fundamental gap, we propose the primal-dual Halpern-PAGE (PD-HP) algorithm. As a purely single-loop method, PD-HP completely bypasses the computational burden of nested iterations. At each step, it merely requires solving a simple strongly convex surrogate subproblem alongside a straightforward dual projection, making it exceptionally efficient and convenient to implement. Crucially, we prove that this computationally lightweight algorithm achieves the optimal $\mathcal{O}(\epsilon^{-3})$ sample complexity for mixed-constrained stochastic weakly convex problems, successfully matching the theoretical lower bounds. Furthermore, when the primal domain is a compact polyhedral convex set, we establish the deterministic stability of the dual multipliers by exploiting the generalized Mangasarian-Fromovitz constraint qualification (MFCQ) alongside Hoffman's error bound. This ensures that our optimal complexity bound holds strictly under the standard, unbounded KKT residual metric without any theoretical gaps or artificial residual truncations.

math.OC↗

arXiv2026

Prox-PEP: A Proximal Partial Exact Penalty Algorithm for Weakly Convex Stochastic Nonlinear Programming

This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an exact penalty approach, transforming them into inequality constraints with auxiliary slack variables. At each iteration, we construct quadratic approximations for both the objective and the constraint functions to facilitate efficient subproblem computation. By carefully designing the second-order approximation matrices, the subproblem constructed via the augmented Lagrangian function is strictly guaranteed to be strongly convex. Furthermore, we adopt a dynamic strategy for the equality penalty parameter: it monotonically increases up to a predefined threshold and remains constant thereafter. Building upon this algorithmic framework, we establish comprehensive asymptotic complexities. We prove that Prox-PEP achieves an $\mathcal{O}(T^{-1/4})$ average expected oracle complexity for $\epsilon$-KKT stationarity, specifically bounding the squared norm of the gradient of the Moreau envelope of the Lagrangian function, alongside constraint violations and complementarity conditions. Additionally, under standard light-tailed martingale noise assumptions, we derive an $\mathcal{O}(T^{-1/8})$ high-probability convergence bound for the norm of the gradient of the Lagrangian's Moreau envelope, as well as $\mathcal{O}(T^{-1/4})$ high-probability bounds for both constraint violations and complementarity conditions.

math.OC↗

arXiv2026

Stability of Lagrangian Generalized Nash Equilibriums

Lagrangian generalized Nash equilibriums (LGNEs) were introduced by Rockafellar (2024) for a class of generalized Nash equilibrium problems (GNEPs) in which each player's strategy is subject to conic constraints. This paper investigates the stability properties of the LGNE solution set, specifically focusing on the Aubin property, isolated calmness, and Lipschitz continuous single-valued localization. For general conically constrained GNEPs, characterizations of the Aubin property and isolated calmness of the LGNE solution mapping under canonical perturbations are established. These characterizations are formulated using the coderivative and graph derivative of normal cone mappings. Subsequently, these general results are specialized to GNEPs with equality and inequality constraints, yielding explicit characterizations for both the Lipschitz continuous single-valued localization and isolated calmness of the corresponding LGNE solution mapping, which are described by nonsingularity of linear complementarity sytems. For GNEPs with shared conic constraints, the Aubin property and isolated calmness of the consensus LGNE solution mapping--where identical Lagrange multipliers are assigned to the shared constraint--are first characterized. We further analyze the case when the conic constraints are specialized as equalities and inequalities. Finally, for classical conically constrained Nash equilibrium problems, the Aubin property and isolated calmness of the Lagrangian Nash equilibrium solution mapping are also analyzed.

math.OC↗

arXiv2023

A Novel Black Box Process Quality Optimization Approach based on Hit Rate

Hit rate is a key performance metric in predicting process product quality in integrated industrial processes. It represents the percentage of products accepted by downstream processes within a controlled range of quality. However, optimizing hit rate is a non-convex and challenging problem. To address this issue, we propose a data-driven quasi-convex approach that combines factorial hidden Markov models, multitask elastic net, and quasi-convex optimization. Our approach converts the original non-convex problem into a set of convex feasible problems, achieving an optimal hit rate. We verify the convex optimization property and quasi-convex frontier through Monte Carlo simulations and real-world experiments in steel production. Results demonstrate that our approach outperforms classical models, improving hit rates by at least 41.11% and 31.01% on two real datasets. Furthermore, the quasi-convex frontier provides a reference explanation and visualization for the deterioration of solutions obtained by conventional models.

cs.LG↗

arXiv2023

Clear Memory-Augmented Auto-Encoder for Surface Defect Detection

In surface defect detection, due to the extreme imbalance in the number of positive and negative samples, positive-samples-based anomaly detection methods have received more and more attention. Specifically, reconstruction-based methods are the most popular. However, existing methods are either difficult to repair abnormal foregrounds or reconstruct clear backgrounds. Therefore, we propose a clear memory-augmented auto-encoder (CMA-AE). At first, we propose a novel clear memory-augmented module (CMAM), which combines the encoding and memoryencoding in a way of forgetting and inputting, thereby repairing abnormal foregrounds and preserving clear backgrounds. Secondly, a general artificial anomaly generation algorithm (GAAGA) is proposed to simulate anomalies that are as realistic and feature-rich as possible. At last, we propose a novel multi scale feature residual detection method (MSFR) for defect segmentation, which makes the defect location more accurate. Extensive comparison experiments demonstrate that CMA-AE achieves state-of-the-art detection accuracy and shows great potential in industrial applications.

cs.CV↗

arXiv2021

Multiobjective Multitasking Optimization Based on Decomposition with Dual Neighborhoods

This paper proposes a multiobjective multitasking optimization evolutionary algorithm based on decomposition with dual neighborhood. In our proposed algorithm, each subproblem not only maintains a neighborhood based on the Euclidean distance among weight vectors within its own task, but also keeps a neighborhood with subproblems of other tasks. Gray relation analysis is used to define neighborhood among subproblems of different tasks. In such a way, relationship among different subproblems can be effectively exploited to guide the search. Experimental results show that our proposed algorithm outperforms four state-of-the-art multiobjective multitasking evolutionary algorithms and a traditional decomposition-based multiobjective evolutionary algorithm on a set of test problems.

cs.CE↗

arXiv2020

Blessing of dimensionality at the edge

In this paper we present theory and algorithms enabling classes of Artificial Intelligence (AI) systems to continuously and incrementally improve with a-priori quantifiable guarantees - or more specifically remove classification errors - over time. This is distinct from state-of-the-art machine learning, AI, and software approaches. Another feature of this approach is that, in the supervised setting, the computational complexity of training is linear in the number of training samples. At the time of classification, the computational complexity is bounded by few inner product calculations. Moreover, the implementation is shown to be very scalable. This makes it viable for deployment in applications where computational power and memory are limited, such as embedded environments. It enables the possibility for fast on-line optimisation using improved training samples. The approach is based on the concentration of measure effects and stochastic separation theorems and is illustrated with an example on the identification faulty processes in Computer Numerical Control (CNC) milling and with a case study on adaptive removal of false positives in an industrial video surveillance and analytics system.

cs.LG↗

arXiv2015

The Gradient Superconvergence of Bilinear Finite Volume Element for Elliptic Problems

We study the gradient superconvergence of bilinear finite volume element (FVE) solving the elliptic problems. First, a superclose weak estimate is established for the bilinear form of the FVE method. Then, we prove that the gradient approximation of the FVE solution has the superconvergence property: $\max_{P\in S}|(\nabla u-\overline{\nabla}u_h)(P)|=O(h^2)|\ln h|$, where $\overline{\nabla}u_h(P)$ denotes the average gradient on elements containing point $P$ and $S$ is the set of optimal stress points composed of the mesh points, the midpoints of edges and elements.

math.NA↗