Related papers: Minimizing a Sum of Clipped Convex Functions

In this paper, we study a class of problems where the sum of truncated convex functions is minimized. In statistical applications, they are commonly encountered when $\ell_0$-penalized models are fitted and usually lead to NP-Hard…

Numerous machine learning and industrial problems can be modeled as the minimization of a sum of $N$ so-called clipped convex functions (SCC), i.e. each term of the sum stems as the pointwise minimum between a constant and a convex…

Parallel and cyclic projection algorithms are proposed for minimizing the sum of a finite family of convex functions over the intersection of a finite family of closed convex subsets of a Hilbert space. These algorithms are of…

This paper extends the algorithm schemes proposed in \cite{Nesterov2007a} and \cite{Nesterov2007b} to the minimization of the sum of a composite objective function and a convex function. Two proximal point-type schemes are provided and…

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…

This paper addresses the challenging issue of symmetry in mixed-integer convex optimization problems, which frequently arise in real-world applications such as the unit commitment problem. Although variable aggregation techniques have been…

We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…

The sum of ratios problem has a variety of important applications in economics and management science, but it is difficult to globally solve this problem. In this paper, we consider the minimization problem of a sum of a number of…

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…

A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of…

Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…

We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…

Given an infeasible, unbounded, or pathological convex optimization problem, a natural question to ask is: what is the smallest change we can make to the problem's parameters such that the problem becomes solvable? In this paper, we address…

In this paper we propose a fast optimization algorithm for approximately minimizing convex quadratic functions over the intersection of affine and separable constraints (i.e., the Cartesian product of possibly nonconvex real sets). This…

We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where…

Consider a sum of convex functions, where the only information known about each individual summand is the location of a minimizer. In this work, we give an exact characterization of the set of possible minimizers of the sum. Our results…

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…

We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…

We show that Dykstra's splitting for projecting onto the intersection of convex sets can be extended to minimize the sum of convex functions and a regularizing quadratic. We give conditions for which convergence to the primal minimizer…

We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of…