Jen‐Chih Yao
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View article: Nash Equilibria of Noncooperative/Miexd Differential Games with Density Constraints in Infinite Dimensions
Nash Equilibria of Noncooperative/Miexd Differential Games with Density Constraints in Infinite Dimensions Open
Motivated by Cournot models, this paper proposes novel models of the noncooperative and cooperative differential games with density constraints in infinite dimensions, where markets consist of infinite firms and demand dynamics are governe…
View article: On the Mathematical Impossibility of Safe Universal Approximators
On the Mathematical Impossibility of Safe Universal Approximators Open
We establish fundamental mathematical limits on universal approximation theorem (UAT) system alignment by proving that catastrophic failures are an inescapable feature of any useful computational system. Our central thesis is that for any …
View article: A Quasi-Newton Method to Solve Uncertain Multiobjective Optimization Problems with Uncertainty Set of Finite Cardinality
A Quasi-Newton Method to Solve Uncertain Multiobjective Optimization Problems with Uncertainty Set of Finite Cardinality Open
In this article, we derive an iterative scheme through a quasi-Newton technique to capture robust weakly efficient points of uncertain multiobjective optimization problems under the upper set less relation. It is assumed that the set of un…
View article: Coarse Geometry of Free Products of Metric Spaces
Coarse Geometry of Free Products of Metric Spaces Open
Recently, a notion of the free product $X \ast Y$ of two metric spaces $X$ and $Y$ has been introduced by T. Fukaya and T. Matsuka. In this paper, we study coarse geometric permanence properties of the free product $X \ast Y$. We show that…
View article: Celler:A Genomic Language Model for Long-Tailed Single-Cell Annotation
Celler:A Genomic Language Model for Long-Tailed Single-Cell Annotation Open
Recent breakthroughs in single-cell technology have ushered in unparalleled opportunities to decode the molecular intricacy of intricate biological systems, especially those linked to diseases unique to humans. However, these progressions …
View article: The combination of single-objective nonlinear uncertain optimization and particle swarm algorithm for optimization crop selection
The combination of single-objective nonlinear uncertain optimization and particle swarm algorithm for optimization crop selection Open
In actual agricultural sowing, due to the uncertainty of various concurrent risk types, such as the expected sales volume, yield per mu, planting cost, and selling price of various crops, a single-objective nonlinear uncertainty optimizati…
View article: System of partial differential hemivariational inequalities involving nonlocal boundary conditions
System of partial differential hemivariational inequalities involving nonlocal boundary conditions Open
Let FPT, MNC, HVI, SEPDE, SMHVI, PGCDD, and NLBC represent the fixed point theorem, measure of noncompactness, hemivariational inequality, system of nonlinear evolutionary partial differential equations, system of mixed hemivariational ine…
View article: Forward-Reflected-Backward Algorithms with Double Inertial Extrapolations for Variational Inequalities with Applications to Image Processing
Forward-Reflected-Backward Algorithms with Double Inertial Extrapolations for Variational Inequalities with Applications to Image Processing Open
This paper designs forward-reflected-backward algorithms with two inertial extrapolation steps to solve variational inequalities of quasi-monotone operators. We consider forward-reflected algorithms with two inertial extrapolation steps fo…
View article: Quasi-Newton Method for Set Optimization Problems with Set-Valued Mapping Given by Finitely Many Vector-Valued Functions
Quasi-Newton Method for Set Optimization Problems with Set-Valued Mapping Given by Finitely Many Vector-Valued Functions Open
In this article, we propose a quasi-Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The set-valued objective mapping under consideration is given by a …
View article: Nonlinear Conjugate Gradient Methods for Optimization of Set-Valued Mappings of Finite Cardinality
Nonlinear Conjugate Gradient Methods for Optimization of Set-Valued Mappings of Finite Cardinality Open
This article presents nonlinear conjugate gradient methods for finding local weakly minimal points of set-valued optimization problems under a lower set less ordering relation. The set-valued objective function of the optimization problem …
View article: CAUCHY-SZEGO PROJECTIONS AND RELATED TOPICS
CAUCHY-SZEGO PROJECTIONS AND RELATED TOPICS Open
In this survey article, we give a comprehensive review of Calder´ on-Zygmund operators from the point of view of Cauchy-Szeg¨ o projections and the sharp estimates of the operators in Hardy spaces. Cauchy-Szeg¨ o projections is closed rela…
View article: Perturbation Analysis of Error Bounds for Convex Functions on Banach Spaces
Perturbation Analysis of Error Bounds for Convex Functions on Banach Spaces Open
This paper focuses on the stability of both local and global error bounds for a proper lower semicontinuous convex function defined on a Banach space. Without relying on any dual space information, we first provide precise estimates of err…
View article: Existence of solutions for second-order differential inclusions associated with highly non-semicontinuous multifunctions
Existence of solutions for second-order differential inclusions associated with highly non-semicontinuous multifunctions Open
In this paper we deal with the existence of generalized solutions for the Cauchy problem associated with a second-order differential inclusion, both in explicit and in implicit form. We firstly prove an existence result for an inclusion of…
View article: New Douglas-Rashford Splitting Algorithms for Generalized DC Programming with Applications in Machine Learning
New Douglas-Rashford Splitting Algorithms for Generalized DC Programming with Applications in Machine Learning Open
In this work, we propose some new Douglas-Rashford splitting algorithms for solving a class of generalized DC (difference of convex functions) in real Hilbert spaces. The proposed methods leverage the proximal properties of the nonsmooth c…
View article: Convergence of self-adaptive Tseng-type algorithms for split variational inequalities and fixed point problems
Convergence of self-adaptive Tseng-type algorithms for split variational inequalities and fixed point problems Open
In this paper, we survey iterative algorithms for solving split variational inequalities and fixed point problems in Hilbert spaces. The investigated split problem is involved in two pseudomonotone operators and two pseudocontractive opera…
View article: Second-Order Strong Optimality and Second-Order Duality for Nonsmooth Constrained Multiobjective Fractional Programming Problems
Second-Order Strong Optimality and Second-Order Duality for Nonsmooth Constrained Multiobjective Fractional Programming Problems Open
This paper investigates constrained nonsmooth multiobjective fractional programming problem (NMFP) in real Banach spaces. It derives a quotient calculus rule for computing the first- and second-order Clarke derivatives of fractional functi…
View article: New Results on Ulam Stabilities of Nonlinear Integral Equations
New Results on Ulam Stabilities of Nonlinear Integral Equations Open
This article deals with the study of Hyers–Ulam stability (HU stability) and Hyers–Ulam–Rassias stability (HUR stability) for two classes of nonlinear Volterra integral equations (VIEqs), which are Hammerstein-type integral and Hammerstein…
View article: Global Existence and Uniqueness of Solutions of Integral Equations with Multiple Variable Delays and Integro Differential Equations: Progressive Contractions
Global Existence and Uniqueness of Solutions of Integral Equations with Multiple Variable Delays and Integro Differential Equations: Progressive Contractions Open
In this work, we delve into a nonlinear integral equation (IEq) with multiple variable time delays and a nonlinear integro-differential equation (IDEq) without delay. Global existence and uniqueness (GEU) of solutions of that IEq with mult…
View article: Variational–hemivariational system for contaminant convection–reaction–diffusion model of recovered fracturing fluid
Variational–hemivariational system for contaminant convection–reaction–diffusion model of recovered fracturing fluid Open
This work is devoted to study the convection–reaction–diffusion behavior of contaminant in the recovered fracturing fluid which flows in the wellbore from shale gas reservoir. First, we apply various constitutive laws for generalized non-N…
View article: Editorial: A special issue on mathematical optimization and applications
Editorial: A special issue on mathematical optimization and applications Open
The theory of mathematical optimization is concerned with the study of the minimization of mathematical functions.Usually, the optimization variables are subject to some side conditions or constraints.Optimization methods are now under spo…
View article: Multi-valued variational inclusion problem and convergence analysis
Multi-valued variational inclusion problem and convergence analysis Open
Inthis paper, under some new appropriate conditions imposed on the parameter and mappings i nvolvedi nt her esolvento peratora ssociatedw itha (?,?)-monotone operator, its Lipschitz continuity is proved and an estimate of its Lipschitz con…
View article: Coderivatives with respect to a set of the normal cone mappings and their applications
Coderivatives with respect to a set of the normal cone mappings and their applications Open
Establishing explicit formulas of coderivatives with respect to a set of the normal cone mapping to a polyhedron, the solution set of a variational inequalities system, is one of the main goals of this paper. By using our coderivative form…
View article: Two nonmonotone multiobjective memory gradient algorithms
Two nonmonotone multiobjective memory gradient algorithms Open
In this paper, two types of nonmonotone memory gradient algorithm for solving unconstrained multiobjective optimization problems are introduced. Under some suitable conditions, we show the convergence of the full sequence generated by the …