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In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
Sparsity constrained minimization captures a wide spectrum of applications in both machine learning and signal processing. This class of problems is difficult to solve since it is NP-hard and existing solutions are primarily based on…
We apply a novel optimization scheme from the image processing and machine learning areas, a fast Primal-Dual method, to achieve controllable and realistic fluid simulations. While our method is generally applicable to many problems in…
Fluid flow simulation is a highly active area with applications in a wide range of engineering problems and interactive systems. Meshless methods like the Moving Particle Semi-implicit (MPS) are a great alternative to deal efficiently with…
Based on the gradient flow, we propose a new method to determine the bounce configuration for false vacuum decay. Our method is applicable to a large class of models with multiple fields. Since the bounce is a saddle point of an action, a…
The article proposes a Caputo fractional conjugate gradient (CFCG) method for unconstrained optimization problems which is applicable to smooth as well as non-smooth problmes. The proposed method uses a non-adaptive version of the Caputo…
Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. The computational complexity of VCSPs depends on the set of allowed cost functions in the input. Recently, the computational…
In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…
We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
Hyperbolic spaces have increasingly been recognized for their outstanding performance in handling data with inherent hierarchical structures compared to their Euclidean counterparts. However, learning in hyperbolic spaces poses significant…
We investigate a variational approach to nonpotential perturbations of gradient flows of nonconvex energies in Hilbert spaces. We prove existence of solutions to elliptic-in-time regularizations of gradient flows by combining the…
Inactive constraints do not contribute to the solution of an optimal control problem, but increase the problem size and burden the numerical computations. We present a novel strategy for handling inactive constraints efficiently by…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
In this paper, we revisit the computation of controlled invariant sets for linear discrete-time systems through a trajectory-based viewpoint. We begin by introducing the notion of convex feasible points, which provides a new…
Convex relaxations of non-convex optimal power flow (OPF) problems have recently attracted significant interest. While existing relaxations globally solve many OPF problems, there are practical problems for which existing relaxations fail…
This paper concerns a new class of discontinuous dynamical systems for constrained optimization. These dynamics are particularly suited to solve nonlinear, non-convex problems in closed-loop with a physical system. Such approaches using…
Fast and stable fluid simulations are an essential prerequisite for applications ranging from computer-generated imagery to computer-aided design in research and development. However, solving the partial differential equations of…
A general, variational approach to derive low-order reduced systems for nonlinear systems subject to an autonomous forcing, is introduced. The approach is based on the concept of optimal parameterizing manifold (PM) that substitutes the…