Related papers: An Adaptive Phase-Field Method for Structural Topo…
We aim to solve a topology optimization problem where the distribution of material in the design domain is represented by a density function. To obtain candidates for local minima, we want to solve the first order optimality system via…
Multi-material structural topology and shape optimization problems are formulated within a phase field approach. First-order conditions are stated and the relation of the necessary conditions to classical shape derivatives are discussed. An…
We develop approximation algorithms for set-selection problems with deterministic constraints, but random objective values, i.e., stochastic probing problems. When the goal is to maximize the objective, approximation algorithms for probing…
This work concerns a structural topology optimisation problem for 4D printing based on the phase field approach. The concept of 4D printing as a targeted evolution of 3D printed structures can be realised in a two-step process. One first…
Although adaptive optimization algorithms have been successful in many applications, there are still some mysteries in terms of convergence analysis that have not been unraveled. This paper provides a novel non-convex analysis of adaptive…
A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the…
We investigate a fixed domain approach in shape optimization, using a regularization of the Heaviside function both in the cost functional and in the state system. We consider the compliance minimization problem in linear elasticity, a well…
We propose adaptive, line search-free second-order methods with optimal rate of convergence for solving convex-concave min-max problems. By means of an adaptive step size, our algorithms feature a simple update rule that requires solving…
The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…
This paper introduces a novel adaptive framework for processing dynamic flow signals over simplicial complexes, extending classical least-mean-squares (LMS) methods to high-order topological domains. Building on discrete Hodge theory, we…
Building upon recent works on linesearch-free adaptive proximal gradient methods, this paper proposes adaPG$^{q,r}$, a framework that unifies and extends existing results by providing larger stepsize policies and improved lower bounds.…
In this paper, approximation schemes are proposed for handling load uncertainty in compliance-based topology optimization problems, where the uncertainty is described in the form of a set of finitely many loading scenarios. Efficient…
A general adaptive refinement strategy for solving linear elliptic partial differential equation with random data is proposed and analysed herein. The adaptive strategy extends the a posteriori error estimation framework introduced by…
In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…
In this paper, we design and analyze a new family of adaptive subgradient methods for solving an important class of weakly convex (possibly nonsmooth) stochastic optimization problems. Adaptive methods that use exponential moving averages…
We propose an efficient probabilistic method to solve a deterministic problem -- we present a randomized optimization approach that drastically reduces the enormous computational cost of optimizing designs under many load cases for both…
Adaptive Finite Element Method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property…
In this work, we investigate a nonconforming finite element approximation of phase-field parameterized topology optimization governed by the Stokes flow. The phase field, the velocity field and the pressure field are approximated by…