Efficiently Optimizing over (Non-Convex) Cones via Approximate Projections

Cone characterizations of approximate solutions in real-vector optimization

Borrowing concepts from linear algebra and convex analysis, it has been shown how the feasible set for a general vector optimization problem can be mapped under a linear transformation so that Pareto points in the image correspond to nondominated solutions for the original problem. The focus of this paper is to establish corresponding results for approximate nondominated points, based on a new ...

Finding Approximate Convex Shapes in RGBD Images

We propose a novel method to find approximate convex 3D shapes from single RGBD images. Convex shapes are more general than cuboids, cylinders, cones and spheres. Many real-world objects are nearconvex and every non-convex object can be represented using convex parts. By finding approximate convex shapes in RGBD images, we extract important structures of a scene. From a large set of candidates ...

Bornological Completion of Locally Convex Cones

In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.

Some Results on Boundedness in Locally Convex Cones

Escaping the Local Minima via Simulated Annealing: Optimization of Approximately Convex Functions

We consider the problem of optimizing an approximately convex function over a bounded convex set in Rn using only function evaluations. The problem is reduced to sampling from an approximately log-concave distribution using the Hit-and-Run method, which is shown to have the same O∗ complexity as sampling from log-concave distributions. In addition to extend the analysis for log-concave distribu...