Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.

Improving ultimate convergence of an augmented Lagrangian method

Optimization methods that employ the classical Powell-Hestenes-Rockafellar augmented Lagrangian are useful tools for solving nonlinear programming problems. Their reputation decreased in the last 10 years due to the comparative success of interior-point Newtonian algorithms, which are asymptotically faster. In this research, a combination of both approaches is evaluated. The idea is to produce a competitive method, being more robust and efficient than its `pure` counterparts for critical problems. Moreover, an additional hybrid algorithm is defined, in which the interior-point method is replaced by the Newtonian resolution of a Karush-Kuhn-Tucker (KKT) system identified by the augmented Lagrangian algorithm. The software used in this work is freely available through the Tango Project web page:http://www.ime.usp.br/similar to egbirgin/tango/.

The bound quiver of a split extension

In this paper, we give a sufficient (which is also necessary under a compatibility hypothesis) condition on a set of arrows in the quiver of an algebra A so that A is a split extension of A/M, where M is the ideal of A generated by the classes of these arrows. We also compare the notion of split extension with that of semiconvex extension of algebras.

Purification and partial characterization of a midgut membrane-bound alpha-glucosidase from Quesada gigas (Hemiptera: Cicadidae)

Adults of Quesada gigas (Hemiptera: Cicadidae) have a major alpha-glucosidase bound to the perimicrovillar membranes, which are lipoprotein membranes that surround the midgut cell microvilli in Hemiptera and Thysanoptera. Determination of the spatial distribution of alpha-glucosidases in Q. gigas midgut showed that this activity is not equally distributed between soluble and membrane-bound isoforms. The major membrane-bound enzyme was solubilized in the detergent Triton X-100 and purified to homogeneity by means of gel filtration on Sephacryl S-100, and ion-exchange on High Q and Mono Q columns. The purified alpha-glucosidase is a protein with a pH optimum of 6.0 against the synthetic substrate p-nitrophenyl alpha-D-glucoside and M(r) of 61,000 (SDS-PAGE). Taking into account V(Max)/K(M) ratios, the enzyme is more active on maltose than sucrose and prefers oligomaltodextrins up to maltopentaose, with lower efficiency for longer chain maltodextrins. The Q gigas alpha-glucosidase was immunolocalized in perimicrovillar membranes by using a monospecific polyclonal antibody raised against the purified enzyme from Dysdercus peruvianus. The role of this enzyme in xylem fluid digestion and its possible involvement in osmoregulation is discussed. (C) 2009 Elsevier Inc. All rights reserved.

Pharmacogenetics of Warfarin: Development of a Dosing Algorithm for Brazilian Patients

A dosing algorithm including genetic (VKORC1 and CYP2C9 genotypes) and nongenetic factors (age, weight, therapeutic indication, and cotreatment with amiodarone or simvastatin) explained 51% of the variance in stable weekly warfarin doses in 390 patients attending an anticoagulant clinic in a Brazilian public hospital. The VKORC1 3673G>A genotype was the most important predictor of warfarin dose, with a partial R(2) value of 23.9%. Replacing the VKORC1 3673G>A genotype with VKORC1 diplotype did not increase the algorithm`s predictive power. We suggest that three other single-nucleotide polymorphisms (SNPs) (5808T>G, 6853G>C, and 9041G>A) that are in strong linkage disequilibrium (LD) with 3673G>A would be equally good predictors of the warfarin dose requirement. The algorithm`s predictive power was similar across the self-identified ""race/color"" subsets. ""Race/color"" was not associated with stable warfarin dose in the multiple regression model, although the required warfarin dose was significantly lower (P = 0.006) in white (29 +/- 13 mg/week, n = 196) than in black patients (35 +/- 15 mg/week, n = 76).

Signal Processing and patternrecognition algorithm for monitoringParkinson’s disease.

This masters thesis describes the development of signal processing and patternrecognition in monitoring Parkison’s disease. It involves the development of a signalprocess algorithm and passing it into a pattern recogniton algorithm also. Thesealgorithms are used to determine , predict and make a conclusion on the study ofparkison’s disease. We get to understand the nature of how the parkinson’s disease isin humans.

Solving the Vehicle Routing Problem with Genetic ALgorithm and Simulated Annealing

This Thesis Work will concentrate on a very interesting problem, the Vehicle Routing Problem (VRP). In this problem, customers or cities have to be visited and packages have to be transported to each of them, starting from a basis point on the map. The goal is to solve the transportation problem, to be able to deliver the packages-on time for the customers,-enough package for each Customer,-using the available resources- and – of course - to be so effective as it is possible.Although this problem seems to be very easy to solve with a small number of cities or customers, it is not. In this problem the algorithm have to face with several constraints, for example opening hours, package delivery times, truck capacities, etc. This makes this problem a so called Multi Constraint Optimization Problem (MCOP). What’s more, this problem is intractable with current amount of computational power which is available for most of us. As the number of customers grow, the calculations to be done grows exponential fast, because all constraints have to be solved for each customers and it should not be forgotten that the goal is to find a solution, what is best enough, before the time for the calculation is up. This problem is introduced in the first chapter: form its basics, the Traveling Salesman Problem, using some theoretical and mathematical background it is shown, why is it so hard to optimize this problem, and although it is so hard, and there is no best algorithm known for huge number of customers, why is it a worth to deal with it. Just think about a huge transportation company with ten thousands of trucks, millions of customers: how much money could be saved if we would know the optimal path for all our packages.Although there is no best algorithm is known for this kind of optimization problems, we are trying to give an acceptable solution for it in the second and third chapter, where two algorithms are described: the Genetic Algorithm and the Simulated Annealing. Both of them are based on obtaining the processes of nature and material science. These algorithms will hardly ever be able to find the best solution for the problem, but they are able to give a very good solution in special cases within acceptable calculation time.In these chapters (2nd and 3rd) the Genetic Algorithm and Simulated Annealing is described in details, from their basis in the “real world” through their terminology and finally the basic implementation of them. The work will put a stress on the limits of these algorithms, their advantages and disadvantages, and also the comparison of them to each other.Finally, after all of these theories are shown, a simulation will be executed on an artificial environment of the VRP, with both Simulated Annealing and Genetic Algorithm. They will both solve the same problem in the same environment and are going to be compared to each other. The environment and the implementation are also described here, so as the test results obtained.Finally the possible improvements of these algorithms are discussed, and the work will try to answer the “big” question, “Which algorithm is better?”, if this question even exists.

A Genetic Algorithm for Solar Boat

Genetic algorithm has been widely used in different areas of optimization problems. Ithas been combined with renewable energy domain, photovoltaic system, in this thesis.To participate and win the solar boat race, a control program is needed and C++ hasbeen chosen for programming. To implement the program, the mathematic model hasbeen built. Besides, the approaches to calculate the boundaries related to conditionhave been explained. Afterward, the processing of the prediction and real time controlfunction are offered. The program has been simulated and the results proved thatgenetic algorithm is helpful to get the good results but it does not improve the resultstoo much since the particularity of the solar driven boat project such as the limitationof energy production

University Scheduling using Genetic Algorithm

The automated timetabling and scheduling is one of the hardest problem areas. This isbecause of constraints and satisfying those constraints to get the feasible and optimizedschedule, and it is already proved as an NP Complete (1) [1]. The basic idea behind this studyis to investigate the performance of Genetic Algorithm on general scheduling problem underpredefined constraints and check the validity of results, and then having comparative analysiswith other available approaches like Tabu search, simulated annealing, direct and indirectheuristics [2] and expert system. It is observed that Genetic Algorithm is good solutiontechnique for solving such problems and later analysis will prove this argument. The programis written in C++ and analysis is done by using variation in various parameters.

University Timetabling using Genetic Algorithm

The field of automated timetabling and scheduling meeting all the requirementsthat we call constraints is always difficult task and already proved as NPComplete. The idea behind my research is to implement Genetic Algorithm ongeneral scheduling problem under predefined constraints and check the validityof results, and then I will explain the possible usage of other approaches likeexpert systems, direct heuristics, network flows, simulated annealing and someother approaches. It is observed that Genetic Algorithm is good solutiontechnique for solving such problems. The program written in C++ and analysisis done with using various tools explained in details later.