arXiv subjects

Chengmiao Yang

Publications and source records attributed to Chengmiao Yang.

3 recordsLinked to original sources

arXiv2025

The charnes--cooper transformation and fractional programs with convex polynomials

This paper proposes a scheme based on the Charnes--Cooper transformation for solving a class of fractional programs with convex polynomial data. We employ the high-degree perturbation method to construct relaxations based on sums of squares for the fractional programs under consideration. Under suitable conditions, we establish results on solution existence, strong duality, asymptotic convergence, and solution extraction. As a special case, fractional programs with SOS-convex polynomial data are also studied.

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arXiv2025

First-order SDSOS-convex semi-algebraic optimization and exact SOCP relaxations

In this paper, we define a new type of nonsmooth convex function, called {\em first-order SDSOS-convex semi-algebraic function}, which is an extension of the previously proposed first-order SDSOS-convex polynomials (Chuong et al. in J Global Optim 75:885--919, 2019). This class of nonsmooth convex functions contains many well-known functions, such as the Euclidean norm, the $\ell_1$-norm commonly used in compressed sensing and sparse optimization, and the least squares function frequently employed in machine learning and regression analysis. We show that, under suitable assumptions, the optimal value and optimal solutions of first-order SDSOS-convex semi-algebraic programs can be found by exactly solving an associated second-order cone programming problem. Finally, an application to robust optimization with first-order SDSOS-convex polynomials is discussed.

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arXiv2024

A parameter-free approach for solving SOS-convex semi-algebraic fractional programs

In this paper, we study a class of nonsmooth fractional programs {\rm (FP, for short)} with SOS-convex semi-algebraic functions. Under suitable assumptions, we derive a strong duality result between the problem (FP) and its semidefinite programming (SDP) relaxations. Remarkably, we extract an optimal solution of the problem (FP) by solving one and only one associated SDP problem. Numerical examples are also given.

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