Related papers: Topology optimization method with nonlinear diffus…
As the capabilities of additive manufacturing techniques increase, topology optimization provides a promising approach to design geometrically sophisticated structures which can be directly manufactured. Traditional topology optimization…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
We consider a distributed stochastic optimization problem in networks with finite number of nodes. Each node adjusts its action to optimize the global utility of the network, which is defined as the sum of local utilities of all nodes.…
In this work, we develop an adaptive nonconforming finite element algorithm for the numerical approximation of phase-field parameterized topology optimization governed by the Stokes system. We employ the conforming linear finite element…
Topology optimization methods face serious challenges when applied to structural design with fluid-structure interaction (FSI) loads, specially for high Reynolds fluid flow. This paper devises an explicit boundary method that employs…
In this paper, distributed convex optimization problem over non-directed dynamical networks is studied. Here, networked agents with single-integrator dynamics are supposed to rendezvous at a point that is the solution of a global convex…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
An Euler discretization of the Langevin diffusion is known to converge to the global minimizers of certain convex and non-convex optimization problems. We show that this property holds for any suitably smooth diffusion and that different…
This work presents an overview of several nonlinear reduction strategies for data compression from various research fields, and a comparison of their performance when applied to problems characterized by diffusion and/or advection terms. We…
We develop a new consensus-based distributed algorithm for solving learning problems with feature partitioning and non-smooth convex objective functions. Such learning problems are not separable, i.e., the associated objective functions…
Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…
Solving statistical learning problems often involves nonconvex optimization. Despite the empirical success of nonconvex statistical optimization methods, their global dynamics, especially convergence to the desirable local minima, remain…
We propose a neural network-based approach to topology optimization that aims to reduce the use of support structures in additive manufacturing. Our approach uses a network architecture that allows the simultaneous determination of an…
Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…
A framework for topology optimization of cooling channels is proposed, which paves the way towards automated design of additively-manufactured cooling channels, required in applications such as the efficient heat management of die casting…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
We consider the tensorial diffusion equation, and address the discrete maximum-minimum principle of mixed finite element formulations. In particular, we address non-negative solutions (which is a special case of the maximum-minimum…
Point-like topological defects are singular configurations that occur in a variety of in and out of equilibrium systems with two-dimensional orientational order. As they are associated with a nonzero circuitation condition, the presence of…
This paper presents a general description of a parameter estimation inverse problem for systems governed by nonlinear differential equations. The inverse problem is presented using optimal control tools with state constraints, where the…
Although traditional optimization methods focus on finding a single optimal solution, most objective functions in modern machine learning problems, especially those in deep learning, often have multiple or infinite numbers of optima.…