SIAM Journal on Optimization

We study the variable metric forward-backward splitting algorithm for convex minimization problems without the standard assumption of the Lipschitz continuity of the gradient. In this setting, we prove that, by requiring only mild assumptions on the ...

This paper formalizes a family of prioritized multicriteria optimization problems and assesses the corresponding up-to-date known suboptimal solutions. The resulting framework is then employed to characterize and search for Boolean functions which are ...

We introduce and analyze stochastic optimization methods where the input to each update is perturbed by bounded noise. We show that this framework forms the basis of a unified approach to analyzing asynchronous implementations of stochastic optimization ...

We propose an optimization model using a novel robust preference relationship---reference-based almost stochastic dominance (RSD). The concept of RSD addresses the two problems in utility-based decision making: (i) ambiguity and inaccuracy in ...

In this paper we study distributionally robust stochastic programming in a setting where there is a specified reference probability measure and the uncertainty set of probability measures consists of measures in some sense close to the reference measure. We ...

In this paper we study the problem of recovering a structured but unknown parameter $\bm{\theta}^*$ from $n$ nonlinear observations of the form $y_i=f(\langle\bm{x}_i,\bm{\theta}^*\rangle)$ for $i=1,2,\ldots,n$. We develop a framework for characterizing ...

We present two algorithms for large-scale noisy low-rank Euclidean distance matrix completion problems, based on semidefinite optimization. Our first method works by relating cliques in the graph of the known distances to faces of the positive semidefinite ...

In this paper, we provide two types of sufficient conditions for ensuring the quadratic growth conditions of a class of constrained convex symmetric and nonsymmetric matrix optimization problems regularized by nonsmooth spectral functions. These ...

Fixed point iterations play a central role in the design and the analysis of a large number of optimization algorithms. We study a new iterative scheme in which the update is obtained by applying a composition of quasi-nonexpansive operators to a point in the ...

We study sum of squares (SOS) relaxations to optimize polynomial functions over a set ${\mathcal V}\cap {\mathbb R}^n$, where ${\mathcal V}$ is a complex algebraic variety. We propose a new methodology that, rather than relying on some algebraic description,...

In this paper, we focus on vector equilibrium problems whose final space is a real linear space not necessarily endowed with a topology. In this framework, some exact and approximate Ekeland variational principles are obtained. The main mathematical tool ...

An estimation problem of fundamental interest is that of phase (or angular) synchronization, in which the goal is to recover a collection of phases (or angles) using noisy measurements of relative phases (or angle offsets). It is known that in the Gaussian ...

In two recent papers regularization methods based on Taylor polynomial models for minimization were proposed that only rely on Hölder conditions on the higher-order employed derivatives. Grapiglia and Nesterov considered cubic regularization with a ...

The paper deals with some theoretical and numerical aspects for an optimal matching problem with constraints. It is known that the uniqueness of the optimal matching measure does not hold even with $L^p$ sources and targets. In this paper, the uniqueness ...

The envelope formula is obtained for optimization problems with positively homogeneous convex functionals defined on a space of random variables. Those problems include linear regression with general error measures and optimal portfolio selection with the ...

We present a simple approach to an analysis of higher order approximations to sets and functions. The objects we study are not of a specific order; they include objects of order 2 and $m$ with $m$ not necessarily an integer. We deduce from these concepts ...

Loosely speaking, causal transport plans are a relaxation of adapted processes in the same sense as Kantorovich transport plans extend Monge-type transport maps. The corresponding causal version of the transport problem has recently been introduced by ...

Many applications in the areas of production, signal processing, economics, bioinformatics, and statistical learning involve a given partial order on certain parameters and a set of noisy observations of the parameters. The goal is to derive estimated ...

This paper considers the problem of distributed optimization over time-varying graphs. For the case of undirected graphs, we introduce a distributed algorithm, referred to as DIGing, based on a combination of a distributed inexact gradient method and a ...

We introduce a new class of convex penalty functions, called variational Gram functions (VGFs), that can promote pairwise relations, such as orthogonality, among a set of vectors in a vector space. These functions can serve as regularizers in convex ...