arXiv subjects

Chengmiao Yang

Publications and source records attributed to Chengmiao Yang.

5 recordsLinked to original sources

arXiv2026

A bounded degree SDSOS hierarchy for solving SPLD polynomial programs

A polynomial optimization problem is said to have an SPLD structure if the polynomials defining its objective and constraints admit decompositions into separable and nonseparable parts, with the maximum degree of the separable parts exceeding that of the nonseparable parts. In this paper, we propose a bounded degree SDSOS hierarchy for globally solving a class of such problems. We establish the asymptotic convergence of this hierarchy over compact feasible sets and provide a sufficient condition for its finite convergence. Numerical experiments compare the proposed hierarchy with the BSDSOS hierarchy (Chuong et al. in J. Global Optim., 75(4):885-919, 2019).

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arXiv2026

Optimality and Exact Moment-SDP Formulations for Robust Two-Stage Convex Polynomial Multiobjective Optimization

In this paper, we study Geoffrion properly efficient solutions of affinely adjustable robust two-stage convex polynomial multiobjective optimization problems with spectrahedral uncertainty. For convex polynomial data, we establish sufficient optimality conditions and necessary conditions under a Slater condition. Under SOS-convexity, we obtain an exact SOS characterization of proper efficiency. Using strictly positive weighted-sum scalarization, we develop a finite-dimensional moment-SDP formulation and establish its optimal-value exactness under the strict feasibility condition. We further establish the recovery results connecting Geoffrion properly efficient solutions with moment-SDP optimal solutions.

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arXiv2026

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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