Search results for "Quadratic Programming"
showing 10 items of 27 documents
A fuzzy ranking strategy for portfolio selection applied to the Spanish stock market
2007
In this paper we present a fuzzy ranking procedure for the portfolio selection problem. The uncertainty on the returns of each portfolio is approximated by means of a trapezoidal fuzzy number. The expected return and risk of the portfolio are then characteristics of that fuzzy number. A rank index that accounts for both expected return and risk is defined, allowing the decision-maker to compare different portfolios. The paper ends with an application of that fuzzy ranking strategy to the Spanish stock market.
2020
This work introduces a method to estimate reflectance, shading, and specularity from a single image. Reflectance, shading, and specularity are intrinsic images derived from the dichromatic model. Estimation of these intrinsic images has many applications in computer vision such as shape recovery, specularity removal, segmentation, or classification. The proposed method allows for recovering the dichromatic model parameters thanks to two independent quadratic programming steps. Compared to the state of the art in this domain, our approach has the advantage to address a complex inverse problem into two parallelizable optimization steps that are easy to solve and do not require learning. The p…
Linear fusion of interrupted reports in cooperative spectrum sensing for cognitive radio networks
2015
Interrupted reporting has recently been introduced as an effective method to increase the energy efficiency of cooperative spectrum sensing schemes in cognitive radio networks. In this paper, joint optimization of the reporting and fusion phases in a cooperative sensing with interrupted reporting is considered. This optimization aims at finding the best weights used at the fusion center to construct a linear fusion of the received interrupted reports, jointly with Bernoulli distributions governing the statistical behavior of the interruptions. The problem is formulated by using the deflection criterion and as a nonconvex quadratic program which is then solved for a suboptimal solution, in a…
Direct Numerical Methods for Optimal Control Problems
2003
Development of interior point methods for linear and quadratic programming problems occurred during the 1990’s. Because of their simplicity and their convergence properties, interior point methods are attractive solvers for such problems. Moreover, extensions have been made to more general convex programming problems.
A Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing
2006
Our goal is to identify the volatility function in Dupire's equation from given option prices. Following an optimal control approach in a Lagrangian framework, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian - to ensure that every SQP step is a descent direction - and implement a line search strategy. In each level of the SQP method a linear-quadratic optimal control problem with box constraints is solved by a primal-dual active set strategy. This guarantees L^1 constraints for the volatility, in particular assuring its positivity. The proposed algorithm is founded on a thorough first- and second-order optimality analysis. We prove the existe…
Frictionless contact-detachment analysis: iterative linear complementarity and quadratic programming approaches.
2012
The object of the paper concerns a consistent formulation of the classical Signorini’s theory regarding the frictionless contact problem between two elastic bodies in the hypothesis of small displacements and strains. The employment of the symmetric Galerkin boundary element method, based on boundary discrete quantities, makes it possible to distinguish two different boundary types, one in contact as the zone of potential detachment, called the real boundary, the other detached as the zone of potential contact, called the virtual boundary. The contact-detachment problem is decomposed into two sub-problems: one is purely elastic, the other regards the contact condition. Following this method…
A bilateral convergent bounding technique for plastic deformations
1990
For the class of elastic perfectly plastic discrete structures, subjected to a dynamic loading history, a bilateral bounding technique for plastic deformations has been studied. The computation of the bound is founded on the concept that to obtain it, any history of fictitious plastic deformations can be used, if only admissible. Such history is obtained by solving a sequence of linear programming problems (LPPs) with a multiple step compared to the step of the sequence of the quadratic programming problems (QPPs) adopting in the classic elasto-plastic analysis. The constraints of the LPPs coincide with the constraints of the QPPs, while the objective function is a linear combination of var…
Fuzzy Mathematical Programming for Portfolio Management
2000
The classical portfolio selection problem was formulated by Markowitz in the 1950s as a quadratic programming problem in which the risk variance is minimized. Since then, many other models have been considered and their associated mathematical programming formulations can be viewed as dynamic, stochastic or static decision problems. In our opinion, the model formulation depends essentially on two factors: the data nature and the treatment given to the risk and return goals. In this communication, we consider several approaches to deal with the data uncertainty for different classical formulations of the portfolio problem. We make use of duality theory and fuzzy programming techniques to ana…
Robust Predictive Control of a variable speed wind turbine using the LMI formalism
2014
This paper proposes a Robust Fuzzy Multivariable Model Predictive Controller (RFMMPC) using Linear Matrix Inequalities (LMIs) formulation. The main idea is to solve at each time instant, an LMI optimization problem that incorporates input, output and Constrained Receding Horizon Predictive Control (CRHPC) constraints, and plant uncertainties, and guarantees certain robustness properties. The RFMMPC is easily designed by solving a convex optimization problem subject to LMI conditions. Then, the derived RFMMPC applied to a variable wind turbine with blade pitch and generator torque as two control inputs. The effectiveness of the proposed design is shown by simulation results.
Solving some optimal control problems using the barrier penalty function method
2005
In this paper we present a new approach to solve the two-level optimization problem arising from an approximation by means of the finite element method of optimal control problems governed by unilateral boundary value problems. The minimized functional depends on control variables and state variables x. The latter are the optimal solution of an auxiliary quadratic programming problem, whose parameters depend on u.