Related papers: Convex hull algorithms based on some variational m…

An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…

In this paper, we propose to exploit the rich hierarchical features of deep convolutional neural networks to improve the accuracy and robustness of visual tracking. Deep neural networks trained on object recognition datasets consist of…

Convex optimizers have known many applications as differentiable layers within deep neural architectures. One application of these convex layers is to project points into a convex set. However, both forward and backward passes of these…

Traditional nearest points methods use all the samples in an image set to construct a single convex or affine hull model for classification. However, strong artificial features and noisy data may be generated from combinations of training…

In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…

We present a new fully dynamic algorithm for maintaining convex hulls under insertions and deletions while supporting geometric queries. Our approach combines the logarithmic method with a deletion-only convex hull data structure, achieving…

We envision programmable matter as a system of nano-scale agents (called particles) with very limited computational capabilities that move and compute collectively to achieve a desired goal. We use the geometric amoebot model as our…

In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…

Segmentation of overlapping convex objects has various applications, for example, in nanoparticles and cell imaging. Often the segmentation method has to rely purely on edges between the background and foreground making the analyzed images…

Imprecise measurements of a point set P = (p1, ..., pn) can be modelled by a family of regions F = (R1, ..., Rn), where each imprecise region Ri contains a unique point pi. A retrieval models an accurate measurement by replacing an…

This paper proposes a variational framework for multi-objective level set topology optimization. The approach interprets the level set function as a generalized coordinate of a fictitious material and derives its equation of motion from…

Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…

We study the minimization of a rank-one quadratic with indicators and show that the underlying set function obtained by projecting out the continuous variables is supermodular. Although supermodular minimization is, in general, difficult,…

Given a set of $n$ points $P$ in the plane, the first layer $L_1$ of $P$ is formed by the points that appear on $P$'s convex hull. In general, a point belongs to layer $L_i$, if it lies on the convex hull of the set $P \setminus…

In this paper, we propose a method for image-set classification based on convex cone models. Image set classification aims to classify a set of images, which were usually obtained from video frames or multi-view cameras, into a target…

This paper analyzes the convex hull of the parametric curve $\left(t, t^2, \cdots, t^N\right)$, where $t$ is in a closed interval. It finds that every point in the convex hull is representable as a convex combination of $\frac{N+1}{2}$…

Detecting out-of-distribution (OOD) data is a critical task for maintaining model reliability and robustness. In this study, we propose a novel anomaly detection algorithm that leverages the convex hull (CH) property of a dataset by…

In the noisy primitives model, each primitive comparison performed by an algorithm, e.g., testing whether one value is greater than another, returns the incorrect answer with random, independent probability p < 1/2 and otherwise returns a…

We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…

We analyze the correctness of an O(n log n) time divide-and-conquer algorithm for the convex hull problem when each input point is a location determined by a normal distribution. We show that the algorithm finds the convex hull of such…