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Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate.…
We consider optimization of composite objective functions, i.e., of the form $f(x)=g(h(x))$, where $h$ is a black-box derivative-free expensive-to-evaluate function with vector-valued outputs, and $g$ is a cheap-to-evaluate real-valued…
This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…
In this paper, we study the iteration complexity of cubic regularization of Newton method for solving composite minimization problems with uniformly convex objective. We introduce the notion of second-order condition number of a certain…
Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems.…
It has been widely recognized that the 0/1 loss function is one of the most natural choices for modelling classification errors, and it has a wide range of applications including support vector machines and 1-bit compressed sensing. Due to…
The minimization of a nonconvex composite function can model a variety of imaging tasks. A popular class of algorithms for solving such problems are majorization-minimization techniques which iteratively approximate the composite nonconvex…
This paper proposes two proximal Newton-CG methods for convex nonsmooth optimization problems in composite form. The algorithms are based on a a reformulation of the original nonsmooth problem as the unconstrained minimization of a…
We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…
In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…
These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…
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…
We propose new iterative methods for computing nontrivial extremal generalized singular values and vectors. The first method is a generalized Davidson-type algorithm and the second method employs a multidirectional subspace expansion…
We develop two new stochastic Gauss-Newton algorithms for solving a class of non-convex stochastic compositional optimization problems frequently arising in practice. We consider both the expectation and finite-sum settings under standard…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
We study the theoretical convergence properties of random-search methods when optimizing non-convex objective functions without having access to derivatives. We prove that standard random-search methods that do not rely on second-order…
A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…