On the Complexity of Optimization over the Standard Simplex

We review complexity results for minimizing polynomials over the standard simplex and unit hypercube.In addition, we show that there exists a polynomial time approximation scheme (PTAS) for minimizing Lipschitz continuous functions and functions with uniformly bounded Hessians over the standard simplex.This extends an earlier result by De Klerk, Laurent and Parrilo [A PTAS for the minimization of polynomials of fixed degree over the simplex, Theoretical Computer Science, to appear.]global optimization;standard simplex;PTAS;multivariate Bernstein approximation;semidefinite programming

Optimization of Univariate Functions on Bounded Intervals by Interpolation and Semidefinite Programming

AMS classifications: 65D05; 65K05; 90C22;

On the Complexity of Optimization over the Standard Simplex

We review complexity results for minimizing polynomials over the standard simplex and unit hypercube.In addition, we show that there exists a polynomial time approximation scheme (PTAS) for minimizing Lipschitz continuous functions and functions with uniformly bounded Hessians over the standard simplex.This extends an earlier result by De Klerk, Laurent and Parrilo [A PTAS for the minimization of polynomials of fixed degree over the simplex, Theoretical Computer Science, to appear.]

Crossed testicular ectopia: a case report and review of the literature

Crossed testicular ectopia (CTE) is an extremely rare anomaly in which deviation of testicular descent results in unilateral location of both testes. It is usually associated with an inguinal hernia, with the spermatic cord of the ectopic testis originating from the appropriate side. Most often the diagnosis of CTE is not made until surgical exploration. We report a case of CTE in a 2-year-old boy who presented with left-sided inguinal hernia with concurrent nonpalpable right testis. Diagnosis was made during diagnostic laparoscopy followed by left open inguinal exploration during which high ligation of the left hernia and trans-septal orchiopexy, contralateral transposition tension-free for each testis was done