相关论文: Safe Peeling for L0-Regularized Least-Squares with…

We consider minimizing a conic quadratic objective over a polyhedron. Such problems arise in parametric value-at-risk minimization, portfolio optimization, and robust optimization with ellipsoidal objective uncertainty; and they can be…

We present a hierarchy of tractable relaxations to obtain lower bounds on the minimum value of a polynomial over a constraint set defined by polynomial equations. In contrast to previous convex relaxation techniques for this problem, our…

Given a digraph $D$, the Minimum Leaf Out-Branching problem (MinLOB) is the problem of finding in $D$ an out-branching with the minimum possible number of leaves, i.e., vertices of out-degree 0. We prove that MinLOB is polynomial-time…

Boolean quadratic optimization problems occur in a number of applications. Their mixed integer-continuous nature is challenging, since it is inherently NP-hard. For this motivation, semidefinite programming relaxations (SDR's) are proposed…

Point containment queries on trimmed surfaces are fundamental to CAD modeling, solid geometry processing, and surface tessellation. Existing approaches such as ray casting and generalized winding numbers often face limitations in robustness…

We propose the first general and practical framework to design certifiable algorithms for robust geometric perception in the presence of a large amount of outliers. We investigate the use of a truncated least squares (TLS) cost function,…

We propose a Binary Robust Least Squares (BRLS) model that encompasses key robust least squares formulations, such as those involving uncertain binary labels and adversarial noise constrained within a hypercube. We show that the geometric…

Layer pruning offers a promising alternative to standard structured pruning, effectively reducing computational costs, latency, and memory footprint. While notable layer-pruning approaches aim to detect unimportant layers for removal, they…

We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…

We present an efficient algorithm for the least squares parameter fitting optimized for component separation in multi-frequency CMB experiments. We sidestep some of the problems associated with non-linear optimization by taking advantage of…

We develop efficient algorithms for optimizing piecewise smooth (PWS) functions where the underlying partition of the domain into smooth pieces is \emph{unknown}. For PWS functions satisfying a quadratic growth (QG) condition, we propose a…

We propose an efficient hybrid least squares/gradient descent method to accelerate DeepONet training. Since the output of DeepONet can be viewed as linear with respect to the last layer parameters of the branch network, these parameters can…

In this paper, we propose an efficient algorithm for the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network…

We present a novel method for solving square jigsaw puzzles based on global optimization. The method is fully automatic, assumes no prior information, and can handle puzzles with known or unknown piece orientation. At the core of the…

The multiway-cut problem is, given a weighted graph and k >= 2 terminal nodes, to find a minimum-weight set of edges whose removal separates all the terminals. The problem is NP-hard, and even NP-hard to approximate within 1+delta for some…

Pruning encompasses a range of techniques aimed at increasing the sparsity of neural networks (NNs). These techniques can generally be framed as minimizing a loss function subject to an $L_0$ norm constraint. This paper introduces CoNNect,…

In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…

Spreading the information over all coefficients of a representation is a desirable property in many applications such as digital communication or machine learning. This so-called antisparse representation can be obtained by solving a convex…

We introduce a cutting-plane framework for nonconvex quadratic programs (QPs) that progressively tightens convex relaxations. Our approach leverages the doubly nonnegative (DNN) relaxation to compute strong lower bounds and generate…

A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…