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The charnes--cooper transformation and fractional programs with convex polynomials
Chengmiao Yang, Liguo Jiao, Jae Hyoung Lee
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 perturbat…
First-order SDSOS-convex semi-algebraic optimization and exact SOCP relaxations
Chengmiao Yang, Liguo Jiao, Jae Hyoung Lee
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 fi…
SPLD polynomial optimization and bounded degree SOS hierarchies
Liguo Jiao, Jae Hyoung Lee, Nguyen Bui Nguyen Thao
In this paper, we introduce a new class of structured polynomials, called separable plus lower degree (SPLD) polynomials. The formal definition of an SPLD polynomial, which extends…
A parameter-free approach for solving SOS-convex semi-algebraic fractional programs
Chengmiao Yang, Liguo Jiao, Jae Hyoung Lee
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 dual…
A new scheme for approximating the weakly efficient solution set of vector rational optimization problems
Feng Guo, Liguo Jiao
In this paper, we provide a new scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set…
On continuous selections of polynomial functions
Feng Guo, Liguo Jiao, Do Sang Kim
A continuous selection of polynomial functions is a continuous function whose domain can be partitioned into finitely many pieces on which the function coincides with a polynomial.…