separating hyperplane – Optimization Online

Zero-Convex Functions, Perturbation Resilience, and Subgradient Projections for Feasibility-Seeking Methods

Published: 2014/05/06

Constrained Nonlinear Optimization, Convex Optimization feasibility problem, nonconvex, perturbation resilience, perturbations, separating hyperplane, stability, subdifferential, subgradient projection method, superiorization, voronoi function, zero-convexity

The convex feasibility problem (CFP) is at the core of the modeling of many problems in various areas of science. Subgradient projection methods are important tools for solving the CFP because they enable the use of subgradient calculations instead of orthogonal projections onto the individual sets of the problem. Working in a real Hilbert space, … Read more

Separation of convex polyhedral sets with uncertain data

Published: 2007/02/28

Milan Hladik

Convex and Nonsmooth Optimization, Robust Optimization convex polyhedra, interval analysis, linear interval equation, linear interval inequalities, separating hyperplane

This paper is a contribution to the interval analysis and separability of convex sets. Separation is a familiar principle and is often used not only in optimization theory, but in many economic applications as well. In real problems input data are usually not known exactly. For the purpose of this paper we assume that data … Read more