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In conventional spectral/finite element methods, the triangulation/quadrilateralization of the domain produces many interior edges which require additional DOF. What if we could directly use the original hull without going to…
In this paper, a modified BFGS algorithm is proposed. The modified BFGS matrix estimates a modified Hessian matrix which is a convex combination of an identity matrix for the steepest descent algorithm and a Hessian matrix for the Newton…
In this paper, we study two general classes of optimization algorithms for kernel methods with convex loss function and quadratic norm regularization, and analyze their convergence. The first approach, based on fixed-point iterations, is…
The problem considered in this paper is the weighted obnoxious facility location in the convex hull of demand points. The objective function is to maximize the smallest weighted distance between a facility and a set of demand points. Three…
Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which…
Current state-of-the-art methods for solving discrete optimization problems are usually restricted to convex settings. In this paper, we propose a general approach based on cutting planes for solving nonlinear, possibly nonconvex, binary…
The present work investigates the segmentation of textures by formulating it as a strongly convex optimization problem, aiming to favor piecewise constancy of fractal features (local variance and local regularity) widely used to model…
The primary goal in cluster analysis is to discover natural groupings of objects. The field of cluster analysis is crowded with diverse methods that make special assumptions about data and address different scientific aims. Despite its…
This survey reviews a clustering method based on solving a convex optimization problem. Despite the plethora of existing clustering methods, convex clustering has several uncommon features that distinguish it from prior art. The…
We propose a localized approach to multiple kernel learning that can be formulated as a convex optimization problem over a given cluster structure. For which we obtain generalization error guarantees and derive an optimization algorithm…
We introduce a new methodology dubbed ``safe peeling'' to accelerate the resolution of L0-regularized least-squares problems via a Branch-and-Bound (BnB) algorithm. Our procedure enables to tighten the convex relaxation considered at each…
Finding a good classifier is a multiobjective optimization problem with different error rates and the costs to be minimized. The receiver operating characteristic is widely used in the machine learning community to analyze the performance…
Deep learning harnesses massive parallel floating-point processing to train and evaluate large neural networks. Trends indicate that deeper and larger neural networks with an increasing number of parameters achieve higher accuracy than…
While Structure from Motion (SfM) achieves great success in 3D reconstruction, it still meets challenges on large scale scenes. In this work, large scale SfM is deemed as a graph problem, and we tackle it in a divide-and-conquer manner.…
This work puts forward a form finding problem of designing a least-volume vault that is a surface structure spanning over a plane region, which via pure compression transfers a vertically tracking load to the supporting boundary. Through a…
In this paper we consider non-smooth convex optimization problems with (possibly) infinite intersection of constraints. In contrast to the classical approach, where the constraints are usually represented as intersection of simple sets,…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
Two characteristics that make convex decomposition algorithms attractive are simplicity of operations and generation of parallelizable structures. In principle, these schemes require that all coordinates update at the same time, i.e., they…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
Active set method aims to find the correct active set of the optimal solution and it is a powerful method for solving strictly convex quadratic problem with bound constraints. To guarantee the finite step convergence, the existing active…