Parametric Active Set Methods (PASM) are a relatively new class of methods to solve convex Quadratic Programming (QP) problems. They are based on tracing the solution along a linear homotopy between a QP with known solution and the QP to be solved. We explicitly identify numerical challenges in PASM and develop strategies to meet these … Read more
The Douglas-Rachford algorithm is a popular iterative method for finding a zero of a sum of two maximal monotone operators defined on a Hilbert space. In this paper, we propose an extension of this algorithm including inertia parameters and develop parallel versions to deal with the case of a sum of an arbitrary number of … Read more
Current successful methods for solving semidefinite programs, SDP, are based on primal-dual interior-point approaches. These usually involve a symmetrization step to allow for application of Newton’s method followed by block elimination to reduce the size of the Newton equation. Both these steps create ill-conditioning in the Newton equation and singularity of the Jacobian of the … Read more
We present a biased random-key genetic algorithm (BRKGA) for finding small covers of computationally difficult set covering problems that arise in computing the 1-width of incidence matrices of Steiner triple systems. Using a parallel implementation of the BRKGA, we compute improved covers for the two largest instances in a standard set of test problems used … Read more
We employ recent work on computational noise to obtain near-optimal finite difference estimates of the derivatives of a noisy function. Our analysis employs a stochastic model of the noise without assuming a specific form of distribution. We use this model to derive theoretical bounds for the errors in the difference estimates and obtain an easily … Read more
We present a novel approach for solving dense saddle-point linear systems in a distributed-memory environment. This work is motivated by an application in stochastic optimization problems with recourse, but the proposed approach can be used for a large family of dense saddle-point systems, in particular those arising in convex programming. Although stochastic optimization problems have … Read more
Although stochastic programming is a powerful tool for modeling decision-making under uncertainty, various impediments have historically prevented its wide-spread use. One key factor involves the ability of non-specialists to easily express stochastic programming problems as extensions of deterministic models, which are often formulated first. A second key factor relates to the difficulty of solving stochastic … Read more
This work gives an overview over the major codes available for the solution of linear semidefinite (SDP) and second-order cone (SOCP) programs. Some developments since the 7th DIMACS Challenge [9, 17] are pointed out as well as some currently under way. Instead of presenting per- formance tables, reference is made to the ongoing benchmark [19] … Read more
An artificial neural network (ANN) is a computational model – implemented as a computer program – that is aimed at emulating the key features and operations of biological neural networks. ANNs are extensively used to model unknown or unspecified functional relationships between the input and output of a “black box” system. In order to apply … Read more
We have developed a new financial indicator – called the Interest Rate Differential Adjusted for Volatility (IRDAV) measure – to assist investors in currency markets. On a monthly basis, we rank currency pairs according to this measure and generate a basket of pairs with the highest IRDAV values. Under positive market conditions, an IRDAV based … Read more