In this paper, we consider a linear two-stage robust optimization model with a mixed integer recourse problem. Currently, this type of two-stage robust optimization model does not have any exact solution algorithm available. We first present a set of sufficient conditions under which the existence of an optimal solution is guaranteed. Then, we present a … Read more
Estimating parameters from data is a key stage of the modelling process, particularly in biological systems where many parameters need to be estimated from sparse and noisy data sets. Over the years, a variety of heuristics have been proposed to solve this complex optimisation problem, with good results in some cases yet with limitations in … Read more
In this paper we discuss time consistency of risk averse multistage stochastic programming problems. We show, in a framework of finite scenario trees, that composition of law invariant coherent risk measures can be law invariant only for the expectation or max-risk measures. CitationPreprintArticleDownload View PDF
In this paper we discuss risk neutral and risk averse approaches to multistage (linear) stochastic programming problems based on the Stochastic Dual Dynamic Programming (SDDP) method. We give a general description of the algorithm and present computational studies related to planning of the Brazilian interconnected power system. Citation ArticleDownload View PDF
The reformulation-linearization technique (RLT), introduced in [W.P. Adams, H.D. Sherali, A tight linearization and an algorithm for zero-one quadratic programming problems, Management Science, 32(10):1274–1290, 1986], provides a way to compute linear programming bounds on the optimal values of NP-hard combinatorial optimization problems. In this paper we show that, in the presence of suitable algebraic symmetry … Read more
This work is devoted to the study of existence and stability results of semidefinite linear complementarity problems (SDLCP). Our approach consists of approximating the variational inequality formulation of the SDLCP by a sequence of suitable chosen variational inequalities. This provides particular estimates for the asymptotic cone of the solution set of the SDLCP. We thus … Read more
This paper is devoted to the study of the {symmetric cone linear complementarity problem} (SCLCP). In this context, our aim is to characterize the class Q_b in terms of larger classes, such as Q and R_0. For this, we introduce the class F and García’s transformations. We studied them for concrete particular instances (such as … Read more
We present algebraic multilevel preconditioners for linear systems arising from the discretization of systems of coupled elliptic partial differential equations (PDEs). These preconditioners are based on modifications of Schwarz methods and of the smoothed aggregation technique, where the coarsening strategy and the restriction and prolongation operators are defined using a point-based approach with a primary … Read more
Index tracking is a passive investment strategy in which an investor purchases a set of assets to mimic a market index. The tracking error, the difference between the performances of the index and the portfolio, may be minimized by buying all the assets contained in the index. However, this strategy results in a considerable amount … Read more
We propose a framework for building preconditioners for sequences of linear systems of the form $(A+\Delta_k) x_k=b_k$, where $A$ is symmetric positive semidefinite and $\Delta_k$ is diagonal positive semidefinite. Such sequences arise in several optimization methods, e.g., in affine-scaling methods for bound-constrained convex quadratic programming and bound-constrained linear least squares, as well as in trust-region … Read more