Related papers: A variational geometric framework for multi-object…

Differentiable vector graphics have enabled powerful gradient-based optimization of vector primitives directly from raster images. However, existing frameworks formulate this as a flat optimization problem, forcing hundreds to thousands of…

Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…

In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box.…

This paper provides an extended level set (X-LS) based topology optimiza- tion method for multi material design. In the proposed method, each zero level set of a level set function {\phi}ij represents the boundary between materials i and j.…

A functional for joint variational object segmentation and shape matching is developed. The formulation is based on optimal transport w.r.t. geometric distance and local feature similarity. Geometric invariance and modelling of…

In this paper, we investigate whether Variational Principles can be associated with the Helmholtz equation subject to impedance (absorbing) boundary conditions. This model has been extensively studied in the literature from both…

Mixed level orthogonal arrays are basic structures in experimental design. We develop three algorithms that compute Rao and Gilbert-Varshamov type bounds for mixed level orthogonal arrays. The computational complexity of the terms involved…

This article introduces a generalized framework for Decentralized Learning formulated as a Multi-Objective Optimization problem, in which both distributed agents and a central coordinator contribute independent, potentially conflicting…

We provide an abstract framework for optimal goal-oriented adaptivity for finite element methods and boundary element methods in the spirit of [Carstensen et al., Comput. Math. Appl. 67 (2014)]. We prove that this framework covers standard…

We present some first results concerning a gradient-based dynamic approach to multi-objective optimization problems, involving inertial effects. We prove the existence of global solution trajectories for this second-order differential…

Multi-modal multi-objective optimization is to locate (almost) equivalent Pareto optimal solutions as many as possible. While decomposition-based evolutionary algorithms have good performance for multi-objective optimization, they are…

In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set…

We propose a method to modify a polygonal mesh in order to fit the zero-isoline of a level set function by extending a standard body-fitted strategy to a tessellation with arbitrarily-shaped elements. The novel level set-fitted approach, in…

Reference frame optimization is a generic framework to calculate a spatially-varying observer field that views an unsteady fluid flow in a reference frame that is as-steady-as-possible. In this paper, we show that the optimized vector field…

This paper presents a topology optimization framework for structural problems subjected to transient loading. The mechanical model assumes a linear elastic isotropic material, infinitesimal strains, and a dynamic response. The optimization…

Non-stationary extremal dependence, whereby the relationship between the extremes of multiple variables evolves over time, is commonly observed in many environmental and financial data sets. However, most multivariate extreme value models…

In Multi-Task Learning (MTL), tasks may compete and limit the performance achieved on each other, rather than guiding the optimization to a solution, superior to all its single-task trained counterparts. Since there is often not a unique…

Multiobjective optimization (MOO) is prevalent in numerous applications, in which a Pareto front (PF) is constructed to display optima under various preferences. Previous methods commonly utilize the set of Pareto objectives (particles on…

Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…

This paper proposes an efficient algorithm for solving the Hartree--Fock equation combining a multilevel correction scheme with an adaptive refinement technique to improve computational efficiency. The algorithm integrates a multilevel…