Yi-Shuai Niu

Yi-Shuai Niu

Difference-of-Convex (DC) programming, which seeks to minimize a function expressed as the difference of two convex functions, arises in a wide range of applications in machine learning, signal processing, and operations research. A classical and widely used algorithm for solving DC programs is the Difference-of-Convex Algorithm (DCA). In this paper, we revisit DCA from a distinctly DC-specific perspective. We first separate well-definedness from asymptotic convergence and introduce an additional assumption ensuring the solvability of the DCA subproblems, which clarifies why the choice of DC decomposition matters. We then develop a Lyapunov-descent-regularity framework in which the descent estimate is read directly from the convex subproblems and the regularity estimate is verified from DCA optimality conditions. This yields global convergence of the iterates $\{x^k\}$ for both standard and convex-constrained DC programs under either the classical Lojasiewicz subgradient inequality or the broader Kurdyka-Lojasiewicz (KL) property. We further explain how stronger regularity regimes, such as the Polyak-Lojasiewicz (PL) condition, fit into the same framework and sharpen the resulting convergence rates. Consequently, we obtain finite-time, linear, and sublinear rates for objective values and iterates in a way that cleanly separates well-definedness, DCA-specific structure, and KL/PL regularity, and that is readily transferable to DCA-type variants.

Yi-Shuai Niu, Shing-Tung Yau

Polylab is a MATLAB toolbox for multivariate polynomial scalars and polynomial matrices with a unified symbolic-numeric interface across CPU and GPU-oriented backends. The software exposes three aligned classes: MPOLY for CPU execution, MPOLY_GPU as a legacy GPU baseline, and MPOLY_HP as an improved GPU-oriented implementation. Across these backends, Polylab supports polynomial construction, algebraic manipulation, simplification, matrix operations, differentiation, Jacobian and Hessian construction, LaTeX export, CPU-side LaTeX reconstruction, backend conversion, and interoperability with YALMIP and SOSTOOLS. Versions 3.0 and 3.1 add two practically important extensions: explicit variable metadata through vars.id and vars.name, which makes mixed-variable expressions safe even when objects are created independently, and affine-normal direction computation via automatic differentiation, MF-logDet-Exact, and MF-logDet-Stochastic. The toolbox has already been used successfully in prior research applications, and Polylab Version 3.1 adds a new geometry-oriented computational layer on top of a mature polynomial modeling core. This paper documents the architecture and user-facing interface of the software, organizes its functionality by workflow, presents representative MATLAB sessions with actual outputs, and reports reproducible benchmarks. The results show that MPOLY is the right default for lightweight interactive workloads, whereas MPOLY-HP becomes advantageous for reduction-heavy simplification and medium-to-large affine-normal computation; the stochastic log-determinant variant becomes attractive in larger sparse regimes under approximation-oriented parameter choices.

Yu You, Yi-Shuai Niu

In this paper we consider the difference-of-convex (DC) programming problems, whose objective function is the difference of two convex functions. The classical DC Algorithm (DCA) is well-known for solving this kind of problems, which generally returns a critical point. Recently, an inertial DC algorithm (InDCA) equipped with heavy-ball inertial-force procedure was proposed in de Oliveira et al. (Set-Valued and Variational Analysis 27(4):895--919, 2019), which potentially helps to improve both the convergence speed and the solution quality. Based on InDCA, we propose a refined inertial DC algorithm (RInDCA) equipped with enlarged inertial step-size compared with InDCA. Empirically, larger step-size accelerates the convergence. We demonstrate the subsequential convergence of our refined version to a critical point. In addition, by assuming the Kurdyka-Łojasiewicz (KL) property of the objective function, we establish the sequential convergence of RInDCA. Numerical simulations on checking copositivity of matrices and image denoising problem show the benefit of larger step-size.

Yi-Shuai Niu, Wentao Ding, Junpeng Hu et al.

We established a Spatio-Temporal Neural Network, namely STNN, to forecast the spread of the coronavirus COVID-19 outbreak worldwide in 2020. The basic structure of STNN is similar to the Recurrent Neural Network (RNN) incorporating with not only temporal data but also spatial features. Two improved STNN architectures, namely the STNN with Augmented Spatial States (STNN-A) and the STNN with Input Gate (STNN-I), are proposed, which ensure more predictability and flexibility. STNN and its variants can be trained using Stochastic Gradient Descent (SGD) algorithm and its improved variants (e.g., Adam, AdaGrad and RMSProp). Our STNN models are compared with several classical epidemic prediction models, including the fully-connected neural network (BPNN), and the recurrent neural network (RNN), the classical curve fitting models, as well as the SEIR dynamical system model. Numerical simulations demonstrate that STNN models outperform many others by providing more accurate fitting and prediction, and by handling both spatial and temporal data.

Yi-Shuai Niu, Yu You, Wenxu Xu et al.

Sentence compression is an important problem in natural language processing with wide applications in text summarization, search engine and human-AI interaction system etc. In this paper, we design a hybrid extractive sentence compression model combining a probability language model and a parse tree language model for compressing sentences by guaranteeing the syntax correctness of the compression results. Our compression model is formulated as an integer linear programming problem, which can be rewritten as a Difference-of-Convex (DC) programming problem based on the exact penalty technique. We use a well-known efficient DC algorithm -- DCA to handle the penalized problem for local optimal solutions. Then a hybrid global optimization algorithm combining DCA with a parallel branch-and-bound framework, namely PDCABB, is used for finding global optimal solutions. Numerical results demonstrate that our sentence compression model can provide excellent compression results evaluated by F-score, and indicate that PDCABB is a promising algorithm for solving our sentence compression model.

Yi-Shuai Niu, Xi-Wei Hu, Yu You et al.

Sentence compression is an important problem in natural language processing. In this paper, we firstly establish a new sentence compression model based on the probability model and the parse tree model. Our sentence compression model is equivalent to an integer linear program (ILP) which can both guarantee the syntax correctness of the compression and save the main meaning. We propose using a DC (Difference of convex) programming approach (DCA) for finding local optimal solution of our model. Combing DCA with a parallel-branch-and-bound framework, we can find global optimal solution. Numerical results demonstrate the good quality of our sentence compression model and the excellent performance of our proposed solution algorithm.