Related papers: Unique solvability and error analysis of the Lagra…
This paper proposes a partially inexact alternating direction method of multipliers for computing approximate solution of a linearly constrained convex optimization problem. This method allows its first subproblem to be solved inexactly…
The variational iteration method is used to solve nonlinear Volterra integral equations. Two approaches are presented distinguished by the method to compute the Lagrange multiplier.
A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is…
We take a careful look at two approaches to deriving stability criteria for ideal MHD equilibria. One is based on a tedious analysis of the linearized equations of motion, while the other examines the second variation of the MHD Hamiltonian…
Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…
This work introduces a stabilised finite element formulation for the Stokes flow problem with a nonlinear slip boundary condition of friction type. The boundary condition is enforced with the help of an additional Lagrange multiplier and…
We propose an energy-optimized invariant energy quadratization method to solve the gradient flow models in this paper, which requires only one linear energy-optimized step to correct the auxiliary variables on each time step. In addition to…
Based on a characterization of the optimality of a feasible solution of a convex entropy minimization problem, one shows that the feasible solutions obtained using formally the Lagrange multipliers method are optimal.
We consider a stationary variational inequality with gradient constraint and obstacle. We prove that this problem can be described by an equation using a Lagrange multiplier and a characteristic function. The Lagrange multiplier contains…
We study gradient flows of general functionals with linear growth with very weak assumptions. Classical results concerning characterisation of solutions require differentiability of the Lagrangian, as for the time-dependent minimal surface…
In this paper we present a complete iteration complexity analysis of inexact first order Lagrangian and penalty methods for solving cone constrained convex problems that have or may not have optimal Lagrange multipliers that close the…
Computing at the exascale level is expected to be affected by a significantly higher rate of faults, due to increased component counts as well as power considerations. Therefore, current day numerical algorithms need to be reexamined as to…
We propose a sequential homotopy method for the solution of mathematical programming problems formulated in abstract Hilbert spaces under the Guignard constraint qualification. The method is equivalent to performing projected backward Euler…
An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied…
Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to…
We propose a model for the coupling between free fluid and a linearized poro-hyperelastic body. In this model, the Brinkman equation is employed for fluid flow in the porous medium, incorporating inertial effects into the fluid dynamics. A…
We discretize the Lagrange multiplier formulation of the obstacle problem by mixed and stabilized finite element methods. A priori and a posteriori error estimates are derived and numerically verified.
This paper develops a robust fixed time optimization framework for constrained problems that guarantees exact constraint satisfaction and convergence to KKT points within fixed time , independent of initial conditions. The approach treats…
This paper studies matrix constrained polynomial optimization. We investigate how to get explicit expressions for Lagrange multiplier matrices from the first order optimality conditions. The existence of these expressions can be shown under…
Distribution network reconfiguration (DNR) is an effective approach for optimizing distribution network operation. However, the DNR problem is computationally challenging due to the mixed-integer non-convex nature. One feasible approach for…