Related papers: Quadratic Decomposable Submodular Function Minimiz…

Several supermodular losses have been shown to improve the perceptual quality of image segmentation in a discriminative framework such as a structured output support vector machine (SVM). These loss functions do not necessarily have the…

Kohn-Sham Density Functional Theory (KS-DFT) has been traditionally solved by the Self-Consistent Field (SCF) method. Behind the SCF loop is the physics intuition of solving a system of non-interactive single-electron wave functions under…

Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…

In this paper, we propose the primal-dual method of multipliers (PDMM) for distributed optimization over a graph. In particular, we optimize a sum of convex functions defined over a graph, where every edge in the graph carries a linear…

In this paper, we introduce a new class of nonsmooth convex functions called SOS-convex semialgebraic functions extending the recently proposed notion of SOS-convex polynomials. This class of nonsmooth convex functions covers many common…

Symmetric submodular functions are an important family of submodular functions capturing many interesting cases including cut functions of graphs and hypergraphs. Maximization of such functions subject to various constraints receives little…

Dense conditional random fields (CRF) with Gaussian pairwise potentials have emerged as a popular framework for several computer vision applications such as stereo correspondence and semantic segmentation. By modeling long-range…

We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint…

This paper presents a novel approach that combines the Deep Ritz Method (DRM) with Fourier feature mapping to solve minimization problems comprised of multi-well, non-convex energy potentials. These problems present computational challenges…

We propose a scalable method for semi-supervised (transductive) learning from massive network-structured datasets. Our approach to semi-supervised learning is based on representing the underlying hypothesis as a graph signal with small…

The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…

Abstract notions of convexity over the vertices of a graph, and corresponding notions of halfspaces, have recently gained attention from the machine learning community. In this work we study monophonic halfspaces, a notion of graph…

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…

We propose a new majorization-minimization (MM) method for non-smooth and non-convex programs, which is general enough to include the existing MM methods. Besides the local majorization condition, we only require that the difference between…

We present new large-scale algorithms for fitting a subgradient regularized multivariate convex regression function to $n$ samples in $d$ dimensions -- a key problem in shape constrained nonparametric regression with applications in…

We present an efficient algorithm for solving fractional programming problems whose objective functions are the ratio of a low-rank quadratic to a positive definite quadratic with convex constraints. The proposed algorithm for these…

Modeling parts of an optimization problem as an optimal value function that depends on a top-level decision variable is a regular occurrence in optimization and an essential ingredient for methods such as Benders Decomposition. It often…

Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes…

Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…