Related papers: Computing optimal partition problems via Lagrange …
This paper deals with the geometric numerical integration of gradient flow and its application to optimization. Gradient flows often appear as model equations of various physical phenomena, and their dissipation laws are essential.…
The unique solvability and error analysis of the original Lagrange multiplier approach proposed in [8] for gradient flows is studied in this paper. We identify a necessary and sufficient condition that must be satisfied for the nonlinear…
We develop several efficient numerical schemes which preserve exactly the global constraints for constrained gradient flows. Our schemes are based on the SAV approach combined with the Lagrangian multiplier approach. They are as efficient…
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…
Recently, a new Lagrange multiplier approach was introduced by Cheng, Liu and Shen in \cite{cheng2020new}, which has been broadly used to solve various challenging phase field problems. To design original energy stable schemes, they have to…
Receding horizon optimal control problems compute the solution at each time step to operate the system on a near-optimal path. However, in many practical cases, the boundary conditions, such as external inputs, constraint equations, or the…
In this work, we focus on separable convex optimization problems with linear and box constraints and compute the solution in closed-form as a function of some Lagrange multipliers that can be easily computed in a finite number of…
In the second part of this series, we use the Lagrange multiplier approach proposed in the first part \cite{CheS21} to construct efficient and accurate bound and/or mass preserving schemes for a class of semi-linear and quasi-linear…
An iterative optimization approach that simultaneously minimizes the energy and optimizes the Lagrange multipliers enforcing desired constraints is presented. The method is tested on previously established benchmark systems and it is proved…
The numerical approximation of incompressible fluid-structure interaction problems with Lagrange multiplier is generally based on strongly coupled schemes. This delivers unconditional stability but at the expense of solving a…
We propose a new Lagrange Multiplier approach to design unconditional energy stable schemes for gradient flows. The new approach leads to unconditionally energy stable schemes that are as accurate and efficient as the recently proposed SAV…
In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…
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.
This paper develops column partition based distributed schemes for a class of large-scale convex sparse optimization problems, e.g., basis pursuit (BP), LASSO, basis pursuit denosing (BPDN), and their extensions, e.g., fused LASSO. We are…
Building on the previous work of Lee et al. and Ferdinand et al. on coded computation, we propose a sequential approximation framework for solving optimization problems in a distributed manner. In a distributed computation system, latency…
In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with…
Variational problems under uniform quasiconvex constraints on the gradient are studied. In particular, existence of solutions to such problems is proved as well as existence of lagrange multipliers associated to the uniform constraint. They…
Existing gradient coding schemes introduce identical redundancy across the coordinates of gradients and hence cannot fully utilize the computation results from partial stragglers. This motivates the introduction of diverse redundancies…
We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. In comparison with recent advances in this vein, the…
Computing high-quality graph partitions is a challenging problem with numerous applications. In this paper, we present a novel meta-heuristic for the balanced graph partitioning problem. Our approach is based on integer linear programs that…