Related papers: An evolutionary vector-valued variational inequali…
We consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated…
The main goal of this paper is to present the application of a superiorization methodology to solution of variational inequalities. Within this framework a variational inequality operator is considered as a small perturbation of a convex…
In this paper, we establish the evolution variational inequality for the weighted Wasserstein distance, without assuming convexity of domains. Thanks to this evolution variational inequality, we can carry out some arguments with weighted…
Let $\textbf{A}$ be a symmetric convex quadratic form on $\mathbb{R}^{Nn}$ and $\Omega\Subset \mathbb{R}^n$ a bounded convex domain. We consider the problem of existence of solutions $u: \Omega \subset \mathbb{R}^n \longrightarrow…
In this paper, we investigate the existence and uniqueness of solutions for the following model problem, involving singularities and inhomogeneous Robin boundary conditions \begin{equation*} \left\{ \begin{array}{ll}…
Recently, Lobb and Nijhoff initiated the study of variational (Lagrangian) structure of discrete integrable systems from the perspective of multi-dimensional consistency. In the present work, we follow this line of research and develop a…
In this article we prove that the first eigenvalue of the $\infty-$Laplacian $$ \left\{ \begin{array}{rclcl} \min\{ -\Delta_\infty v,\, |\nabla v|-\lambda_{1, \infty}(\Omega) v \} & = & 0 & \text{in} & \Omega v & = & 0 & \text{on} &…
We establish Euler-Lagrange equations for a problem of Calculus of variations where the unknown variable contains a term of delay on a segment.
We get multiplicity of normalized solutions for the fractional Schr\"{o}dinger equation $$ (-\Delta)^su+V(\varepsilon x)u=\lambda u+h(\varepsilon x)f(u)\quad \mbox{in $\mathbb{R}^N$}, \qquad\int_{\mathbb{R}^N}|u|^2dx=a, $$ where…
We present a powerful and easy-to-implement algorithm for solving constrained optimization problems that involve $L_1$/total-variation regularization terms, and both equality and inequality constraints. We discuss the relationship of our…
In this paper we prove the strong convergence of the explicit iterative process to a common fixed point of the finite family of nonexpansive mappings defined on Hilbert space, which solves the the variational inequality on the fixed points…
We consider a Bolza type optimal control problem of the form \begin{equation}\min J_{t}(y,u):=\int_t^T\Lambda(s,y(s), u(s))\,ds+g(y(T))\tag{P$_{t,x}$}\end{equation} Subject to: \begin{equation}\label{tag:admissible}\tag{D}\begin{cases} y\in…
In this paper, we introduce new implicit and explicit iterative schemes which converge strongly to a unique solution of variational inequality problems for strongly accretive operators over a common fixed point set of finite family of…
We present arguments in favour of the inequalities $var(X_n^2|X \in B_v(\rho)) \le 2\lambda_n E[X_n^2|X \in B_v(\rho)]$, where $X \sim N_v(0,\Lambda)$ is a normal vector in $v\ge 1$ dimensions, with zero mean and covariance matrix $\Lambda…
We prove new existence and uniqueness results for weak solutions to non-homogeneous initial-boundary value problems for parabolic equations modeled on the evolution of the p-Laplacian.
We show the validity of select existence results for a vector optimization problem, and a variational inequality. More generally, we consider generalized vector quasi-variational inequalities, as well as, fixed point problems on genuine…
In this article, we study an inverse problem for the following convective Brinkman-Forchheimer (CBF) equations: \begin{align*} \boldsymbol{u}_t-\mu…
In this work, we focus on separable convex optimization problems with box constraints and a set of triangular linear constraints. The solution is given in closed-form as a function of some Lagrange multipliers that can be computed through…
By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…
In this paper, we study a class of non-convex optimization problems known as multi-affine quadratic equality constrained problems, which appear in various applications--from generating feasible force trajectories in robotic locomotion and…