Related papers: A Unifying Modeling Abstraction for Infinite-Dimen…
We study an optimization problem related to the approximation of given data by a linear combination of transformed modes. In the simplest case, the optimization problem reduces to a minimization problem well-studied in the context of proper…
The generalization capability of unsupervised domain adaptation can mitigate the need for extensive pixel-level annotations to train semantic segmentation networks by training models on synthetic data as a source with computer-generated…
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 order to meet the requirements of practical applications, a model of deforming manifold in the embedded space is proposed. The deforming vector and deforming field are presented to precisely describe the deforming process, which have…
Multi-objective optimization problems are ubiquitous in real-world science, engineering and design optimization problems. It is not uncommon that the objective functions are as a black box, the evaluation of which usually involve…
Real-world experiments involve batched & delayed feedback, non-stationarity, multiple objectives & constraints, and (often some) personalization. Tailoring adaptive methods to address these challenges on a per-problem basis is infeasible,…
We show that a broad range of convex optimization algorithms, including alternating projection, operator splitting, and multiplier methods, can be systematically derived from the framework of subspace correction methods via convex duality.…
In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a…
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We…
Temporal abstraction refers to the ability of an agent to use behaviours of controllers which act for a limited, variable amount of time. The options framework describes such behaviours as consisting of a subset of states in which they can…
Solving optimization problems with unknown parameters often requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the…
In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes a reference domain is introduced and it is optimized over a set of…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
This paper connects discrete optimal transport to a certain class of multi-objective optimization problems. In both settings, the decision variables can be organized into a matrix. In the multi-objective problem, the notion of Pareto…
Many real world optimization problems are formulated as mixed-variable optimization problems (MVOPs) which involve both continuous and discrete variables. MVOPs including dimensional variables are characterized by a variable-size search…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…
Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an…
This study demonstrates how the adjoint-based framework traditionally used to compute gradients in PDE optimization problems can be extended to handle general constraints on the state variables. This is accomplished by constructing a…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…