arXiv subjects

Pham Viet Hai

Publications and source records attributed to Pham Viet Hai.

15 recordsLinked to original sources

arXiv2026

Second order continuous and discrete dynamical systems for solving inverse quasi-variational inequalities

In this paper, we investigate the inverse quasi-variational inequality problem in finite-dimensional spaces. First, we introduce a second-order dynamical system whose trajectory converges exponentially to the solution of the inverse quasi-variational inequality, under the assumptions of Lipschitz continuity and strong monotonicity. Next, we discretize the proposed dynamical system to develop an algorithm, and prove that the iterations converge linearly to the unique solution of the inverse quasi-variational inequality. Finally, we present numerical experiments and applications to validate the theoretical results and compare the performance with existing methods.

math.OC↗

arXiv2025

Cyclicity of composition operators on the Paley-Wiener spaces

In this article we characterize the cyclicity of bounded composition operators $C_ϕf=f\circ ϕ$ on the Paley-Wiener spaces of entire functions $B^2_σ$ for $σ>0$. We show that $C_ϕ$ is cyclic precisely when $ϕ(z)=z+b$ where either $b\in\mathbb{C}\setminus\mathbb{R}$ or $b\in\mathbb{R}$ with $0<|b|\leq π/σ$. We also describe when the reproducing kernels of $B^2_σ$ are cyclic vectors for $C_ϕ$ and see that this is related to a question of completeness of exponential sequences in $L^2[-σ,σ]$. The interplay between cyclicity and complex symmetry plays a key role in this work.

math.FA↗

arXiv2024

Second-order dynamical systems with a smoothing effect for solving paramonotone variational inequalities

In this paper, we propose a second-order dynamical system with a smoothing effect for solving paramonotone variational inequalities. Under standard assumptions, we prove that the trajectories of this dynamical system converges to a solution of the variational inequality problem. A time discretization of this dynamical system provides an iterative inertial projection-type method. Our result generalizes and improves the existing results. Some numerical examples are given to confirm the theoretical results and illustrate the effectiveness of the proposed algorithms.

math.OC↗

arXiv2024

A third order dynamical system for generalized monotone equation

We propose a third order dynamical system for solving a nonlinear equation in Hilbert spaces where the operator is cocoercive with respect to the solutions set. Under mild conditions on the parameters, we establish the existence and uniqueness of the generated trajectories as well as its asymptotic convergence to a solution of the equation. When the operator is strongly monotone with respect to the solutions set, we deliver an exponential convergence rate of $e^{-2t}$, which is significantly faster than the known results of second order dynamical systems. In particular, for convex optimization problems, the proposed dynamical system provides a fast convergence rate of {\bf $\mathcal{O}(\frac{1}{t^3})$} for the objective values. In addition, we discuss the applications of the proposed dynamical system to several splitting monotone inclusion problems.

math.OC↗

arXiv2023

Complex symmetry in the Fock space of several variables

In this paper we study the complex symmetry in the several variable Fock space by using the techniques of weighted composition operators and semigroups. We characterize unbounded weighted composition operators that are (real) complex symmetric with respect to a concrete conjugation. Using this characterization, we study complex symmetric semigroups and their generators. We realize such generators as first-order differential operators.

math.FA↗

arXiv2022

Real Symmetric, Unitary, And Complex Symmetric Weighted Composition Operators On Bergman Spaces Of Polydisk

In this paper, we study weighted composition operators on Bergman spaces of analytic functions which are square integrable on polydisk. We develop the study in full generality, meaning that the corresponding weighted composition operators are not assumed to be bounded. The properties of weighted composition operators such as real symmetry, unitariness, complex symmetry, are characterized fully in simple algebraic terms, involving their symbols. As it turns out, a weighted composition operator having a symmetric structure must be bounded. We also obtain the interesting consequence that real symmetric weighted composition operators are complex symmetric corresponding an adapted and highly relevant conjugation.

math.CV↗

arXiv2021

Complex symmetric weighted composition operators on Bergman spaces and Lebesgue spaces

In the paper, we investigate weighted composition operators on Bergman spaces of a half-plane. We characterize weighted composition operators which are hermitian and those which are complex symmetric with respect to a family of conjugations. As it turns out, weighted composition operators enhanced by a symmetry must be bounded. Hermitian, and unitary weighted composition operators are proven to be complex symmetric with respect to an adapted and highly relevant conjugation. We classify which the linear fractional functions give rise to the complex symmetry of bounded composition operators. We end the paper with a natural link to complex symmetry in Lebesgue space.

math.FA↗

arXiv2020

The Gradient descent method from the perspective of fractional calculus

Motivated by gradient methods in optimization theory, we give methods based on $ψ$-fractional derivatives of order $α$ in order to solve unconstrained optimization problems. The convergence of these methods is analyzed in detail. This paper also presents an Adams-Bashforth-Moulton (ABM) method for the estimation of solutions to equations involving $ψ$-fractional derivatives. Numerical examples using the ABM method show that the fractional order $α$ and weight $ψ$ are tunable parameters, which can be helpful for improving the performance of gradient descent methods.

math.OC↗

arXiv2020

Multi-valued weighted composition operators on Fock space

Multivalued linear operators, also known as linear relations, are studied on a specific class of weighted, composition transforms on Fock space. Basic properties of this class of linear relations, such as closed graph, boundedness, complex symmetry, real symmetry, or isometry are characterized in simple algebraic terms, involving their symbols.

math.FA↗

arXiv2020

Complex symmetric evolution equations

We study certain dynamical systems which leave invariant an indefinite quadratic form via semigroups or evolution families of complex symmetric Hilbert space operators. In the setting of bounded operators we show that a $\mathcal{C}$-selfadjoint operator generates a contraction $C_0$-semigroup if and only if it is dissipative. In addition, we examine the abstract Cauchy problem for nonautonomous linear differential equations possessing a complex symmetry. In the unbounded operator framework we isolate the class of \emph{complex symmetric, unbounded semigroups} and investigate Stone-type theorems adapted to them. On Fock space realization, we characterize all $\mathcal{C}$-selfadjoint, unbounded weighted composition semigroups. As a byproduct we prove that the generator of a $\mathcal{C}$-selfadjoint, unbounded semigroup is not necessarily $\mathcal{C}$-selfadjoint.

math.DS↗

arXiv2020

Complex symmetry of first-order differential operators on Hardy space

Given holomorphic functions $ψ_0$ and $ψ_1$, we consider first-order differential operators acting on Hardy space, generated by the formal differential expression $E(ψ_0,ψ_1)f(z)=ψ_0(z)f(z)+ψ_1(z)f'(z)$. We characterize these operators which are complex symmetric with respect to weighted composition conjugations. In parallel, as a basis of comparison, a characterization for differential operators which are hermitian is carried out. Especially, it is shown that hermitian differential operators are contained properly in the class of $\calC$-selfadjoint differential operators. The calculation of the point spectrum of some of these operators is performed in detail.

math.CV↗

arXiv2019

Model and Reinforcement Learning for Markov Games with Risk Preferences

We motivate and propose a new model for non-cooperative Markov game which considers the interactions of risk-aware players. This model characterizes the time-consistent dynamic "risk" from both stochastic state transitions (inherent to the game) and randomized mixed strategies (due to all other players). An appropriate risk-aware equilibrium concept is proposed and the existence of such equilibria is demonstrated in stationary strategies by an application of Kakutani's fixed point theorem. We further propose a simulation-based Q-learning type algorithm for risk-aware equilibrium computation. This algorithm works with a special form of minimax risk measures which can naturally be written as saddle-point stochastic optimization problems, and covers many widely investigated risk measures. Finally, the almost sure convergence of this simulation-based algorithm to an equilibrium is demonstrated under some mild conditions. Our numerical experiments on a two player queuing game validate the properties of our model and algorithm, and demonstrate their worth and applicability in real life competitive decision-making.

cs.GT↗

arXiv2019

Polynomial behavior in mean of stochastic skew-evolution semiflows

In this paper, we are interested in the more general concept of a polynomial (in)stability in mean in which the polynomial behaviour in the classical sense is replaced by a weaker requirement with respect to some probability measure. This concept includes the classical concepts of a polynomial (in)stability as particular cases. Extending techniques employed in the deterministic case, we obtain variants of a well-known theorem of Datko for a polynomial (in)stability in mean. This is done by using the techniques of stochastic skew-evolution semiflows and Banach spaces of functions or sequences.

math.PR↗

arXiv2018

Unbounded Weighted Composition Operators on Fock space

In this paper, we consider \emph{unbounded} weighted composition operators acting on Fock space, and investigate some important properties of these operators, such as $\calC$-selfadjoint (with respect to weighted composition conjugations), Hermitian, normal, cohyponormal, and invertible. In addition, the paper shows that unbounded normal weighted composition operators are contained properly in the class of $\calC$-selfadjoint operators with respect to weighted composition conjugations. The computation of the spectrum is carried out in detail.

math.CV↗

arXiv2018

Complex symmetric differential operators on Fock space

The space of entire functions which are integrable with respect to the Gaussian weight, known also as the Fock space, is one of the preferred functional Hilbert spaces for modelling and experimenting harmonic analysis, quantum mechanics or spectral analysis phenomena. This space of entire functions carries a three parameter family of canonical isometric involutions. We characterize the linear differential operators acting on Fock space which are complex symmetric with respect to these conjugations. In parallel, as a basis of comparison, we discuss the structure of self-adjoint linear differential operators. The computation of the point spectrum of some of these operators is carried out in detail.

math-ph↗