In this paper we first show that the objective function of a leastsquares type nonlinear parameter estimation problem can be any non-negative real function, and therefore this class of problems corre-sponds to global optimization. Two non-derivative implementationsof a global optimization method are presented; with nine standardtest functions applied to measure their eff...

We analyze the consensus based optimization method proposed in Pinnau et al. (2017) one dimension. rigorously provide a quantitative error estimate between point and global minimizer of given objective function. Our analysis covers general functions; we do not require any structural assumption on

Solving inverse problems, in particular inverse scattering problems, parameterfitting procedures are used quite often because the analytical inversion procedures are not available. The general scheme for such procedures is simple: one has a relation B(q) = A, where B is some operator, q is an unknown function, and A is the data. In inverse scattering problems q is a potential, and A is the scat...

We address the issue of computing a global minimizer AC Optimal Power Flow problem. introduce valid inequalities to strengthen Semidefinite Programming relaxation, yielding novel Conic relaxation. Leveraging these constraints, we dynamically generate Mixed-Integer Linear (MILP) relaxations, whose solutions asymptotically converge minimizers apply this iterative MILP scheme on IEEE PES PGLib [2]...

We consider analytical and numerical aspects of the phase diagram for microphase separation of diblock copolymers. Our approach is variational and is based upon a density functional theory which entails minimization of a nonlocal Cahn–Hilliard functional. Based upon two parameters which characterize the phase diagram, we give a preliminary analysis of the phase plane. That is, we divide the pla...

We present a unified framework to analyze the global convergence of Langevin dynamics based algorithms for nonconvex finite-sum optimization with n component functions. At the core of our analysis is a direct analysis of the ergodicity of the numerical approximations to Langevin dynamics, which leads to faster convergence rates. Specifically, we show that gradient Langevin dynamics (GLD) and st...

Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it challenging to apply them to large scale datasets. Moreover, in many applications the data can display structures beyond simply being low-rank, e.g., images and vi...