This contribution focuses on testing the empirical impact of convexity assumption in estimating costs using nonparametric specifications technology and cost functions. Apart from reviewing scant available evidence, results based two publicly data sets reveal effect axiom function estimates: estimates convex technologies turn out to be average between 21% 38% lower than those computed nonconvex ...

We propose a globally convergent numerical method, called the convexification, to numerically compute viscosity solution first-order Hamilton-Jacobi equations through vanishing process where parameter is fixed small number. By we mean that employ suitable Carleman weight function convexify cost functional defined directly from form of equation under consideration. The strict convexity this rigo...

Relaxed damage formulations enable to overcome the mesh dependency induced by a loss of ellipticity. However, such approaches require construction convex hull associated energy potential. Within this contribution, an improved one-dimensional, relaxed formulation [1] with successive, computationally optimal convexification scheme, see [2], is presented. Instead solving non-convex optimization pr...

In this paper, we propose a redistributed proximal bundle method for class of nonconvex nonsmooth optimization problems with inexact information, i.e., consider the problem computing approximate critical points when only information about function values and subgradients are available show that reasonable convergence properties obtained. We assume errors in computation functions bounded princip...

To compute the spatially distributed dielectric constant from backscattering computationally simulated ane experimentally collected data, we study a coefficient inverse problem for 1D hyperbolic equation. solve this problem, establish new version of Carleman estimate and then employ to construct cost functional, which is strictly convex on bounded set an arbitrary diameter in Hilbert space. The...

Convexification based on convex envelopes is ubiquitous in the non-linear optimization literature. Thanks to considerable efforts of community for decades, we are able compute a number functions that appear practice, and thus obtain tight tractable approximations challenging problems. We contribute this line work by considering family that, best our knowledge, has not been considered before cal...

We consider the ensemble clustering problem where the task is to 'aggregate' multiple clustering solutions into a single consolidated clustering that maximizes the shared information among given clustering solutions. We obtain several new results for this problem. First, we note that the notion of agreement under such circumstances can be better captured using an agreement measure based on a 2D...

The motivation for a closer investigation of Dieudonné-Rashevsky type problems (P) is two-fold. First, due to its close affinity to the basic problem of multidimensional calculus of variations, the problem (1.3) − (1.5) is well-suited as a model problem in order to ascertain how the proof of optimality conditions is influenced through the weakening of the convexity properties of the data. Since...

ÐIn this paper, a new method for the estimation of the fundamental matrix from point correspondences is presented. The minimization of the algebraic error is performed while taking explicitly into account the rank-two constraint on the fundamental matrix. It is shown how this nonconvex optimization problem can be solved avoiding local minima by using recently developed convexification technique...