We present a new methodology for the numerical pricing of a class of exotic derivatives such as Asian or barrier options when the underlying asset price dynamics are modelled by a geometric Brownian motion or a number of mean-reverting processes of interest. This methodology identifies derivative prices with infinite-dimensional linear programming problems involving the moments … Read more
We consider the class of nonlinear optimal control problems with all data (differential equation, state and control constraints, cost) being polynomials. We provide a simple hierarchy of LMI-relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value. Preliminary results show that good approximations are obtained with few moments. Citation LAAS … Read more
We study a relative optimization framework for quasi-maximum likelihood blind source separation and relative Newton method as its particular instance. The structure of the Hessian allows its fast approximate inversion. In the second part we present Smoothing Method of Multipliers (SMOM) for minimization of sum of pairwise maxima of smooth functions, in particular sum of … Read more
This paper is concerned with the optimization of continuum structures under dynamic loading using methods from topology design. The constraint functions are non-linear and implicit, their evaluation requires the resolution of a computation-intensive finite-element analysis performed by a black-box commercial structural mechanics software such as MSC/Nastran. We first present a brief overview of topology optimization … Read more
In the recent years, there has been a considerable amount of work in the development of numerical methods for derivative free optimization problems. Some of this work relies on the management of the geometry of sets of sampling points for function evaluation and model building. In this paper, we continue the work developed in [Conn, … Read more
We address a problem of covariance selection, where we seek a trade-off between a high likelihood against the number of non-zero elements in the inverse covariance matrix. We solve a maximum likelihood problem with a penalty term given by the sum of absolute values of the elements of the inverse covariance matrix, and allow for … Read more
The Hartree-Fock method is well known in quantum chemistry, and widely used to obtain atomic and molecular eletronic wave functions, based on the minimization of a functional of the energy. This gives rise to a multi-extremal, nonconvex, polynomial optimization problem. We give a novel mathematical programming formulation of the problem, which we solve by using … Read more
A theory of globally convergent trust-region methods for self-consistent field electronic structure calculations that use the density matrices as variables is developed. The optimization is performed by means of sequential global minimizations of a quadratic model of the true energy. The global minimization of this quadratic model, subject to the idempotency of the density matrix … Read more
The evolutionary history of species may be described by a phylogenetic tree whose topology captures ancestral relationships among the species, and whose branch lengths denote evolution times. For a fixed topology and an assumed probabilistic model of nucleotide substitution, we show that the likelihood of a given tree is a d.c. (difference of convex) function … Read more
We propose minimum volume ellipsoids (MVE) clustering as an alternate clustering technique to k-means clustering for Gaussian data points and explore its value and practicality. MVE clustering allocates data points into clusters that minimizes the total volumes of each cluster’s covering ellipsoids. Motivations for this approach include its scale-invariance, its ability to handle asymmetric and … Read more