Related papers: Efficient Vertex-Oriented Polytopic Projection for…
This paper is devoted to the general problem of projection onto a polyhedral convex cone generated by a finite set of generators.This problem is reformulated into projection onto the polytope obtained by simple truncation of the original…
Variable order structures model situations in which the comparison between two points depends on a point-to-cone map. In this paper, an inexact projected gradient method for solving smooth constrained vector optimization problems on…
In many problems, the inputs arrive over time, and must be dealt with irrevocably when they arrive. Such problems are online problems. A common method of solving online problems is to first solve the corresponding linear program, and then…
We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $\Pi$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem…
We introduce a fixed point iteration process built on optimization of a linear function over a compact domain. We prove the process always converges to a fixed point and explore the set of fixed points in various convex sets. In particular,…
This paper addresses constrained smooth saddle-point problems in settings where projection onto the feasible sets is computationally expensive. We bridge the gap between projection-based and projection-free optimization by introducing a…
We present a new interior-point potential-reduction algorithm for solving monotone linear complementarity problems (LCPs) that have a particular special structure: their matrix $M\in{\mathbb R}^{n\times n}$ can be decomposed as $M=\Phi U +…
This paper primarily focuses on computing the Euclidean projection of a vector onto the $\ell_{p}$ ball in which $p\in(0,1)$. Such a problem emerges as the core building block in statistical machine learning and signal processing tasks…
Vision-Language Pre-Trained models, notably CLIP, that utilize contrastive learning have proven highly adept at extracting generalizable visual features. To inherit the well-learned knowledge of VLP models for downstream tasks, several…
Automating the solutions of multiple network information theory problems, stretching from fundamental concerns such as determining all information inequalities and the limitations of linear codes, to applied ones such as designing coded…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
We present a simple and efficient acceleration technique for an arbitrary method for computing the Euclidean projection of a point onto a convex polytope, defined as the convex hull of a finite number of points, in the case when the number…
In this paper we consider a problem, called convex projection, of projecting a convex set onto a subspace. We will show that to a convex projection one can assign a particular multi-objective convex optimization problem, such that the…
Random projection algorithm is an iterative gradient method with random projections. Such an algorithm is of interest for constrained optimization when the constraint set is not known in advance or the projection operation on the whole…
Online reputation systems are commonly used by e-commerce providers nowadays. In order to generate an objective ranking of online items' quality according to users' ratings, many sophisticated algorithms have been proposed in the…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
Consider a polyhedral convex cone which is given by a finite number of linear inequalities. We investigate the problem to project this cone into a subspace and show that this problem is closely related to linear vector optimization: We…
Methods for Projection Pursuit aim to facilitate the visual exploration of high-dimensional data by identifying interesting low-dimensional projections. A major challenge is the design of a suitable quality metric of projections, commonly…
The interconnection network comprises a significant portion of the cost of large parallel computers, both in economic terms and power consumption. Several previous proposals exploit large-radix routers to build scalable low-distance…
We design an algorithm to compute the Newton polytope of the resultant, known as resultant polytope, or its orthogonal projection along a given direction. The resultant is fundamental in algebraic elimination, optimization, and geometric…