Automatic verification of computer code is of paramount importance in embedded systems supplying essential services. One of the most important verification techniques is static code analysis by abstract interpretation: the concrete semantics of a programming language (i.e.the values $\chi$ that variable symbols {\tt x} appearing in a program can take during its execution) are replaced … Read more
We introduce an algebraic modeling language, named ROME, for a class of robust optimization problems. ROME serves as an intermediate layer between the modeler and optimization solver engines, allowing modelers to express robust optimization problems in a mathematically meaningful way. In this paper, we highlight key features of ROME which expediates the modeling and subsequent … Read more
NOMAD is software that implements the MADS algorithm (Mesh Adaptive Direct Search) for black-box optimization under general nonlinear constraints. Blackbox optimization is about optimizing functions that are usually given as costly programs with no derivative information and no function values returned for a significant number of calls attempted. NOMAD is designed for such problems and … Read more
We review the common fixed point problem for the class of directed operators. This class is important because many commonly used nonlinear operators in convex optimization belong to it. We present our recent definition of sparseness of a family of operators and discuss a string-averaging algorithmic scheme that favorably handles the common fixed points problem … Read more
An algorithm for finding sums of hermitian squares decompositions for polynomials in noncommuting variables is presented. The algorithm is based on the “Newton chip method”, a noncommutative analog of the classical Newton polytope method, and semide finite programming. Citation I. Klep and J. Povh. Semide nite programming and sums of hermitian squares of noncommutative polynomials. J. Pure … Read more
We present a structure-conveying algebraic modelling language for mathematical programming. The proposed language extends AMPL with object-oriented features that allows the user to onstruct models from sub-models, and is implemented as a combination of pre- and post-processing phases for AMPL. Unlike traditional modelling languages, the new approach does not scramble the block structure of the … Read more
SparseCoLO is a Matlab package for implementing the four conversion methods, proposed by Kim, Kojima, Mevissen, and Yamashita, via positive semidefinite matrix completion for an optimization problem with matrix inequalities satisfying a sparse chordal graph structure. It is based on quite a general description of optimization problem including both primal and dual form of linear, … Read more
The solution of trust-region and regularisation subproblems which arise in unconstrained optimization is considered. Building on the pioneering work of Gay, More’ and Sorensen, methods which obtain the solution of a sequence of parametrized linear systems by factorization are used. Enhancements using high-order polynomial approximation and inverse iteration ensure that the resulting method is both … Read more
An Asset-Liability Management model with a novel strategy for controlling risk of underfunding is presented in this paper. The basic model involves multiperiod decisions (portfolio rebalancing) and deals with the usual uncertainty of investment returns and future liabilities. Therefore it is well-suited to a stochastic programming approach. A stochastic dominance concept is applied to measure … Read more
Support Vector Machines are a powerful machine learning technology, but the training process involves a dense quadratic optimization problem and is computationally challenging. A parallel implementation of Support Vector Machine training has been developed, using a combination of MPI and OpenMP. Using an interior point method for the optimization and a reformulation that avoids the … Read more