Related papers: Single-Projection Procedure for Infinite Dimension…
This paper focuses on convex constrained optimization problems, where the solution is subject to a convex inequality constraint. In particular, we aim at challenging problems for which both projection into the constrained domain and a…
We provide formulas for projectors onto a polyhedral set, i.e. the intersection of a finite number of halfspaces. To this aim we formulate the problem of finding the projection as a convex optimization problem and we solve explicitly…
The discretization of least-squares problems for linear ill-posed operator equations in Hilbert spaces is considered. The main subject of this article concerns conditions for convergence of the associated discretized minimum-norm…
We study how the supporting hyperplanes produced by the projection process can complement the method of alternating projections and its variants for the convex set intersection problem. For the problem of finding the closest point in the…
This paper addresses constrained smooth saddle-point problems in settings where projection onto the feasible sets is computationally expensive. We bridge the gap between projection-based and projection-free optimization by introducing a…
This paper considers a networked system with a finite number of users and supposes that each user tries to minimize its own private objective function over its own private constraint set. It is assumed that each user's constraint set can be…
Cutting plane methods, particularly outer approximation, are a well-established approach for solving nonlinear discrete optimization problems without relaxing the integrality of decision variables. While powerful in theory, their…
The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on…
Under investigation is the problem of finding the best approximation of a function in a Hilbert space subject to convex constraints and prescribed nonlinear transformations. We show that in many instances these prescriptions can be…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
This paper is devoted to general nonconvex problems of multiobjective optimization in Hilbert spaces. Based on Mordukhovich's limiting subgradients, we define a new notion of Pareto critical points for such problems, establish necessary…
This paper deals with the convex feasibility problem, where the feasible set is given as the intersection of a (possibly infinite) number of closed convex sets. We assume that each set is specified algebraically as a convex inequality,…
We consider an optimization problem in a convex space $E$ with an affine objective function, subject to $J$ constraints in the forms of inequalities on some other affine functions, where $J$ is a given nonnegative integer. Under suitable…
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…
We model a problem motivated by road design as a feasibility problem. Projections onto the constraint sets are obtained, and projection methods for solving the feasibility problem are studied. We present results of numerical experiments…
We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…
We show that the minimum distance projection in the L1-norm from an interior point onto the boundary of a convex set is achieved by a single, unidimensional projection. Application of this characterization when the convex set is a…
A polyhedral convex set optimization problem is given by a set-valued objective mapping from the $n$-dimensional to the $q$-dimensional Euclidean space whose graph is a convex polyhedron. This problem can be seen as the most elementary…
The problem of the minimization of least squares functionals with $\ell^1$ penalties is considered in an infinite dimensional Hilbert space setting. While there are several algorithms available in the finite dimensional setting there are…