The major focus of this work is to compare several methods for computing the proximal point of a nonconvex function via numerical testing. To do this, we introduce two techniques for randomly generating challenging nonconvex test functions, as well as two very specific test functions which should be of future interest to Nonconvex Optimization Benchmarking. We then compare the effectiveness of ...

Nonconvex optimization problems arise in different research fields and arouse lots of attention in signal processing, statistics and machine learning. In this work, we explore the accelerated proximal gradient method and some of its variants which have been shown to converge under nonconvex context recently. We show that a novel variant proposed here, which exploits adaptive momentum and block ...

Continuous optimization is an important problem in many areas of AI, including vision, robotics, probabilistic inference, and machine learning. Unfortunately, most real-world optimization problems are nonconvex, causing standard convex techniques to find only local optima, even with extensions like random restarts and simulated annealing. We observe that, in many cases, the local modes of the o...

Many optimization problems arising in high-dimensional statistics decompose naturally into a sum of several terms, where the individual terms are relatively simple but the composite objective function can only be optimized with iterative algorithms. In this paper, we are interested in optimization problems of the form F(Kx) + G(x), where K is a fixed linear transformation, while F and G are fun...

Nowadays, asynchronous parallel algorithms have received much attention in the optimization field due to the crucial demands for modern large-scale optimization problems. However, most asynchronous algorithms focus on convex problems. Analysis on nonconvex problems is lacking. For the Asynchronous Stochastic Descent (ASGD) algorithm, the best result from (Lian et al., 2015) can only achieve an ...

MAP inference in continuous probabilistic models has largely been restricted to convex density functions in order to guarantee tractability of the underlying model, since high-dimensional nonconvex optimization problems contain a combinatorial number of local minima, making them extremely challenging for convex optimization techniques. This choice has resulted in significant computational advan...

In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points that are obtained over time through costly observations. This paper presents an optimization framework that takes into account the information collection (ob...

A global optimization based approach for nding all homogeneous azeotropes in multicompo-nent mixtures is presented. The global optimization approach is based on a branch and bound framework in which upper and lower bounds on the solution are reened by successively partitioning the target region into small disjoint rectangles. The objective of such an approach is to locate all global minima sinc...

Although many methods exist for intensity modulated radiotherapy (IMRT) fluence map optimization for crisp data, based on clinical practice, some of the involved parameters are fuzzy. In this paper, the best fluence maps for an IMRT procedure were identifed as a solution of an optimization problem with a quadratic objective function, where the prescribed target dose vector was fuzzy. First, a d...

In this paper we propose a mathematical programming model for a large drinking water supply network and discuss some possible extensions. The proposed optimization model is of a real water distribution network, the largest water supply network in Flanders. The problem is nonlinear, nonconvex and involves some binary variables, making it belong to the class of NP-hard problems. We discuss a way ...