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Topology optimization (TO) has experienced a dramatic development over the last decades aided by the arising of metamaterials and additive manufacturing (AM) techniques, and it is intended to achieve the current and future challenges. In…
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
Over-segmentation into superpixels is a very effective dimensionality reduction strategy, enabling fast dense image processing. The main issue of this approach is the inherent irregularity of the image decomposition compared to standard…
Topology optimization (TO) provides a principled mathematical approach for optimizing the performance of a structure by designing its material spatial distribution in a pre-defined domain and subject to a set of constraints. The majority of…
This paper proposes a two-view deterministic geometric model fitting method, termed Superpixel-based Deterministic Fitting (SDF), for multiple-structure data. SDF starts from superpixel segmentation, which effectively captures prior…
Many large-scale optimization problems decompose into a master problem and scenario subproblems, a structure that can be exploited by Benders decomposition. In Benders decomposition, each iteration may generate many cuts from scenario…
We present a level-set based topology optimization algorithm for design optimization problems involving an arbitrary number of different materials, where the evolution of a design is solely guided by topological derivatives. Our method can…
A theoretical framework and numerical techniques to solve optimal control problems with a spatial trace term in the terminal cost and governed by regularized nonlinear hyperbolic conservation laws are provided. Depending on the spatial…
Overlay network topology together with peer/data organization and search algorithm are the crucial components of unstructured peer-to-peer (P2P) networks as they directly affect the efficiency of search on such networks. Scale-free…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
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…
The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a…
FPGAs are well established in the signal processing domain, where their fine-grained programmable nature allows the inherent parallelism in these applications to be exploited for enhanced performance. As architectures have evolved, FPGA…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…
Tomography is a widely used tool for analyzing microstructures in three dimensions (3D). The analysis, however, faces difficulty because the constituent materials produce similar grey-scale values. Sometimes, this prompts the image…
This article deals with the existence of hypersurfaces minimizing general shape functionals under certain geometric constraints. We consider as admissible shapes orientable hypersurfaces satisfying a so-called reach condition, also known as…
Inverse design algorithms are the basis for realizing high-performance, freeform nanophotonic devices. Current methods to enforce geometric constraints, such as practical fabrication constraints, are heuristic and not robust. In this work,…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
When approaching a clustering problem, choosing the right clustering algorithm and parameters is essential, as each clustering algorithm is proficient at finding clusters of a particular nature. Due to the unsupervised nature of clustering…