Related papers: Solving constrained Procrustes problems: a conic o…

This paper considers mathematical programs, whose constraints are expressed by a parameterized vector equilibrium problem. The latter is a well recognized framework, which is able to cover multicriteria optimization, vector variational…

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…

We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…

In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…

We consider minimizing an objective function subject to constraints defined by the intersection of lower-level sets of convex functions. We study two cases: (i) strongly convex and Lipschitz-smooth objective function and (ii) convex but…

We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…

We provide new gradient-based methods for efficiently solving a broad class of ill-conditioned optimization problems. We consider the problem of minimizing a function $f : \mathbb{R}^d \rightarrow \mathbb{R}$ which is implicitly…

This paper is concerned with the solution of large-scale linear discrete ill-posed problems with error-contaminated data. Tikhonov regularization is a popular approach to determine meaningful approximate solutions of such problems. The…

In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…

Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the…

A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…

Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is…

We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range…

A new and simple method for quasi-convex optimization is introduced from which its various applications can be derived. Especially, a global optimum under constrains can be approximated for all continuous functions.

In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…

We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…

We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly-convex functionals. We develop a family of stochastic…

With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…