Paula Amaral

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We provide Completely Positive and Copositive Optimization formulations for the Constrained Fractional Quadratic Problem (CFQP) and Standard Fractional Quadratic Problem (StFQP). Based on these formulations, Semidefinite Programming (SDP) relaxations are derived for finding good lower bounds to these fractional programs, which can be used in a global(More)
University examination scheduling is a difficult and heavily administrative task, particularly when the number of students and courses is high. Changes in educational paradigms, an increase in the number of students, the aggregation of schools, more flexible curricula, among others, are responsible for an increase in the difficulty of the problem. As a(More)
This paper addresses the problem of finding an optimal correction of an inconsistent linear system, where only the nonzero coefficients of the constraint matrix are allowed to be perturbed for reconstructing a consistent system. Using the Frobenius norm as a measure of the distance to feasibility, a nonconvex minimization problem is formulated, whose(More)
The problem of inconsistency between constraints often arises in practice as the result, among others, of the complexity of real models or due to unrealistic requirements and preferences. To overcome such inconsistency two major actions may be taken: removal of constraints or changes in the coefficients of the model. This last approach, that can be(More)
In this paper, an algorithm is introduced to find an optimal solution for an optimization problem that arises in total least squares with inequality constraints, and in the correction of infeasible linear systems of inequalities. The stated problem is a nonconvex program with a special structure that allows the use of a(More)
We propose a copositive reformulation of the mixed-integer fractional quadratic problem (MIFQP) under general linear constraints. This problem class arises naturally in many applications, e.g., for optimizing communication or social networks, or studying game theory problems arising from genetics. It includes several APX-hard subclasses: the maximum cut(More)
We consider the problem of correcting an inconsistent system of linear inequalities, Ax ≤ b, subject to nonnegativity constraints, x ≥ 0. We formulate this problem as a nonlinear program and derive the corresponding Karush-Kuhn-Tucker conditions. These conditions reveal several interesting properties that solutions must satisfy and allow us to derive(More)
The aim was to assess the presence of smear layer after canal instrumentation with two reciprocating rotary systems and a continuous motion one. Thirty canals were shaped with Reciproc, WaveOne or Mtwo systems. Smear layer was assessed following a three value scale at coronal, middle and apical levels with a scanning electron microscopy. Reciproc scores:(More)
Given an infeasible system of linear inequalities, Ax ≤ b, we address the problem of correcting both the matrix of coefficients A by A + H and vector b by b + p to minimize the Frobenius norm of [H, p]. For a system of linear equations this problem can be solved by an algebraic and well-studied method known as the Total Least Squares. For inequalities,(More)
In this paper, we present an application of Tabu Search (TS) to the examination timetabling problem. One of the drawbacks of this meta-heuristic is related to the need of tuning some parameter (like tabu tenure) whose value affects the performance of the algorithm. The importance of developing an automatic procedure is clear considering that most of the(More)