Intrinsic complexity estimates in polynomial optimization

A pr 2 01 3 Intrinsic complexity estimates in polynomial optimization 1

It is known that point searching in basic semialgebraic sets and the search for globally minimal points in polynomial optimization tasks can be carried out using (s d)O(n) arithmetic operations, where n and s are the numbers of variables and constraints and d is the maximal degree of the polynomials involved. We associate to each of these problems an intrinsic system degree which becomes in wor...

New complexity analysis of a full Nesterov-Todd steps IIPM for semidefinite optimization

New Barrier Parameter Updating Technique in Mehrotra-Type Algorithm

On the Complexity of Non Universal Polynomial Equation Solving: old and new results

These pages summarize some results on the efficiency of polynomial equation solving. We focus on semantic algorithms, i.e., algorithms whose running time depends on some intrinsic/semantic invariant associated with the input data. Both computer algebra and numerical analysis algorithms are discussed. We show a probabilistic and positive answer to Smale’s 17th problem. Estimates of the probabili...

Faber polynomial coefficient estimates for bi-univalent functions defined by subordinations

A function is said to be bi-univalent on the open unit disk D if both the function and its inverse are univalent in D. Not much is known about the behavior of the classes of bi-univalent functions let alone about their coefficients. In this paper we use the Faber polynomial expansions to find coefficient estimates for four well-known classes of bi-univalent functions which are defined by subord...