Linear vs. nonlinear algorithms for linear problems

Fuzzy Primal Simplex Algorithms for Solving Fuzzy Linear Programming Problems

Linear vs. Nonlinear Effects for Nonlinear Schrödinger Equations with Potential

We review some recent results on nonlinear Schrödinger equations with potential, with emphasis on the case where the potential is a second order polynomial, for which the interaction between the linear dynamics caused by the potential, and the nonlinear effects, can be described quite precisely. This includes semi-classical régimes, as well as finite time blow-up and scattering issues. We prese...

Linear-time Algorithms for Pairwise Statistical Problems

Several key computational bottlenecks in machine learning involve pairwise distance computations, including all-nearest-neighbors (finding the nearest neighbor(s) for each point, e.g. in manifold learning) and kernel summations (e.g. in kernel density estimation or kernel machines). We consider the general, bichromatic case for these problems, in addition to the scientific problem of N-body sim...

Approximation Algorithms for Linear Fractional-Multiplicative Problems

In this paper we propose a Fully Polynomial Time Approximation Scheme (FPTAS) for a class of optimization problems where the feasible region is a polyhedral one and the objective function is the sum or product of linear ratio functions. The class includes the well known ones of Linear (Sum-of-Ratios) Fractional Programming and Multiplicative Programming.

Nonlinear Inexact Uzawa Algorithms for Linear and Nonlinear Saddle-point Problems

This paper proposes some nonlinear Uzawa methods for solving linear and nonlinear saddle-point problems. A nonlinear inexact Uzawa algorithm is first introduced for linear saddlepoint problems. Two different PCG techniques are allowed in the inner and outer iterations of the algorithm. This algorithm is then extended for a class of nonlinear saddle-point problems arising from some convex optimi...