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Guoju Ye

Publications and source records attributed to Guoju Ye.

5 recordsLinked to original sources
arXiv2023

Fritz-John optimality condition in fuzzy optimization problems and its application to classification of fuzzy data

The main objective of this paper is to derive the optimality conditions for one type of fuzzy optimization problems. At the beginning, we define a cone of descent direction for fuzzy optimization, and prove that its intersection with the cone of feasible directions at an optimal point is an empty set. Then, we present first-order optimality conditions for fuzzy optimization problems. Furthermore, we generalize the Gordan's theorem for fuzzy linear inequality systems and utilize it to deduce the Fritz-John optimality condition for the fuzzy optimization with inequality constraints. Finally, we apply the optimality conditions established in this paper to a binary classification problem for support vector machines with fuzzy data. In the meantime, numerical examples are described to demonstrate the primary findings proposed in the present paper.

math.OC↗
arXiv2018

Some inequalities for interval-valued functions on time scales

We introduce the interval Darboux delta integral (shortly, the $ID$ $Δ$-integral) and the interval Riemann delta integral (shortly, the $IR$ $Δ$-integral) for interval-valued functions on time scales. Fundamental properties of $ID$ and $IR$ $Δ$-integrals and examples are given. Finally, we prove Jensen's, Hölder's and Minkowski's inequalities for the $IR$ $Δ$-integral. Also, some examples are given to illustrate our theorems.

math.CA↗
arXiv2017

The fuzzy Henstock-Kurzweil delta integral on time scales

We investigate properties of the fuzzy Henstock-Kurzweil delta integral (shortly, FHK $Δ$-integral) on time scales, and obtain two necessary and sufficient conditions for FHK $Δ$-integrability. The concept of uniformly FHK $Δ$-integrability is introduced. Under this concept, we obtain a uniformly integrability convergence theorem. Finally, we prove monotone and dominated convergence theorems for the FHK $Δ$-integral.

math.CA↗
arXiv2017

Existence theorems for a nonlinear second-order distributional differential equation

In this work, we are concerned with existence of solutions for a nonlinear second-order distributional differential equation, which contains measure differential equations and stochastic differential equations as special cases. The proof is based on the Leray--Schauder nonlinear alternative and Kurzweil--Henstock--Stieltjes integrals. Meanwhile, examples are worked out to demonstrate that the main results are sharp.

math.CA↗