Inexact restoration approaches to solve mathematical program with complementarity constraints

Mathematical Program with Complementarity Constraints (MPCC) finds applica- tion in many fields. As the complementarity constraints fail the standard Linear In- dependence Constraint Qualification (LICQ) or the Mangasarian-Fromovitz constraint qualification (MFCQ), at any feasible point, the nonlinear programming theory may not be directly applied to MPCC. However, the MPCC can be reformulated as NLP problem and solved by nonlinear programming techniques. One of them, the Inexact Restoration (IR) approach, performs two independent phases in each iteration - the feasibility and the optimality phases. This work presents two versions of an IR algorithm to solve MPCC. In the feasibility phase two strategies were implemented, depending on the constraints features. One gives more importance to the complementarity constraints, while the other considers the priority of equality and inequality constraints neglecting the complementarity ones. The optimality phase uses the same approach for both algorithm versions. The algorithms were implemented in MATLAB and the test problems are from MACMPEC collection.

A filter inexact-restoration method for nonlinear programming

A new iterative algorithm based on the inexact-restoration (IR) approach combined with the filter strategy to solve nonlinear constrained optimization problems is presented. The high level algorithm is suggested by Gonzaga et al. (SIAM J. Optim. 14:646–669, 2003) but not yet implement—the internal algorithms are not proposed. The filter, a new concept introduced by Fletcher and Leyffer (Math. Program. Ser. A 91:239–269, 2002), replaces the merit function avoiding the penalty parameter estimation and the difficulties related to the nondifferentiability. In the IR approach two independent phases are performed in each iteration, the feasibility and the optimality phases. The line search filter is combined with the first one phase to generate a “more feasible” point, and then it is used in the optimality phase to reach an “optimal” point. Numerical experiences with a collection of AMPL problems and a performance comparison with IPOPT are provided.

A filter algorithm: comparison with NLP solvers

The purpose of this work is to present an algorithm to solve nonlinear constrained optimization problems, using the filter method with the inexact restoration (IR) approach. In the IR approach two independent phases are performed in each iteration—the feasibility and the optimality phases. The first one directs the iterative process into the feasible region, i.e. finds one point with less constraints violation. The optimality phase starts from this point and its goal is to optimize the objective function into the satisfied constraints space. To evaluate the solution approximations in each iteration a scheme based on the filter method is used in both phases of the algorithm. This method replaces the merit functions that are based on penalty schemes, avoiding the related difficulties such as the penalty parameter estimation and the non-differentiability of some of them. The filter method is implemented in the context of the line search globalization technique. A set of more than two hundred AMPL test problems is solved. The algorithm developed is compared with LOQO and NPSOL software packages.

Partial spectral projected gradient method with active-set strategy for linearly constrained optimization

A method for linearly constrained optimization which modifies and generalizes recent box-constraint optimization algorithms is introduced. The new algorithm is based on a relaxed form of Spectral Projected Gradient iterations. Intercalated with these projected steps, internal iterations restricted to faces of the polytope are performed, which enhance the efficiency of the algorithm. Convergence proofs are given and numerical experiments are included and commented. Software supporting this paper is available through the Tango Project web page: http://www.ime.usp.br/similar to egbirgin/tango/.

TWO NEW WEAK CONSTRAINT QUALIFICATIONS AND APPLICATIONS

We present two new constraint qualifications (CQs) that are weaker than the recently introduced relaxed constant positive linear dependence (RCPLD) CQ. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major open question was to identify the exact set of gradients whose properties had to be preserved locally and that would still work as a CQ. This is done in the first new CQ, which we call the constant rank of the subspace component (CRSC) CQ. This new CQ also preserves many of the good properties of RCPLD, such as local stability and the validity of an error bound. We also introduce an even weaker CQ, called the constant positive generator (CPG), which can replace RCPLD in the analysis of the global convergence of algorithms. We close this work by extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods: sequential quadratic programming, augmented Lagrangians, interior point algorithms, and inexact restoration.

Nitrogen dynamics during ecosystem development in tropical forest restoration

We considered whether ecological restoration using high diversity of native tree species serves to restore nitrogen dynamics in the Brazilian Atlantic Forest. We measured delta(15)N and N content in green foliage and soil; vegetation N:P ratio; and soil N mineralization in a preserved natural forest and restored forests of ages 21 and 52 years. Green foliage delta(15)N values, N content, N:P ratio, inorganic N and net mineralization and nitrification rates were all higher, the older the forest. Our findings indicate that the recuperation of N cycling has not been achieved yet in the restored forests even after 52 years, but show that they are following a trajectory of development that is characterized by their N cycling intensity becoming similar to a natural mature forest of the same original forest formation. This study demonstrated that some young restored forests are more limited by N compared to mature natural forests. We document that the recuperation of N cycling in tropical forests can be achieved through ecological restoration actions. (C) 2011 Elsevier B.V. All rights reserved.

A hybrid system for upper limb movement restoration in quadriplegics

Generally, quadriplegic individuals have difficulties performing object manipulation. Toward satisfactory manipulation, reach and grasp movements must be performed with voluntary control, and for that, grasp force feedback is essential. A hybrid system aiming at partial upper limb sensory-motor restoration for quadriplegics was built. Such device is composed of an elbow dynamic orthosis that provides elbow flexion/extension (range was approximately from 20 degrees to 120 degrees, and average angular speed was approximately 15 degrees/s) with forearm support, a wrist static orthosis and neuromuscular electrical stimulation for grasping generation, and a glove with force sensors that allows grasping force feedback. The glove presents two user interface modes: visual by light emitting diodes or audio emitted by buzzer. Voice control of the entire system (elbow dynamic orthosis and electrical stimulator) is performed by the patient. The movements provided by the hybrid system, combined with the scapular and shoulder movements performed by the patient, can aid quadriplegic individuals in tasks that involve reach and grasp movements.

Emerging Threats and Opportunities for Large-Scale Ecological Restoration in the Atlantic Forest of Brazil

Over the past 150 years, Brazil has played a pioneering role in developing environmental policies and pursuing forest conservation and ecological restoration of degraded ecosystems. In particular, the Brazilian Forest Act, first drafted in 1934, has been fundamental in reducing deforestation and engaging private land owners in forest restoration initiatives. At the time of writing (December 2010), however, a proposal for major revision of the Brazilian Forest Act is under intense debate in the National Assembly, and we are deeply concerned about the outcome. On the basis of the analysis of detailed vegetation and hydrographic maps, we estimate that the proposed changes may reduce the total amount of potential areas for restoration in the Atlantic Forest by approximately 6 million hectares. As a radically different policy model, we present the Atlantic Forest Restoration Pact (AFRP), which is a group of more than 160 members that represents one of the most important and ambitious ecological restoration programs in the world. The AFRP aims to restore 15 million hectares of degraded lands in the Brazilian Atlantic Forest biome by 2050 and increase the current forest cover of the biome from 17% to at least 30%. We argue that not only should Brazilian lawmakers refrain from revising the existing Forest Law, but also greatly step up investments in the science, business, and practice of ecological restoration throughout the country, including the Atlantic Forest. The AFRP provides a template that could be adapted to other forest biomes in Brazil and to other megadiversity countries around the world.

Forest restoration in an indigenous land considering a forest remnant influence (Avai, Sao Paulo State, Brazil)

The expansion of agricultural and pasture areas over native forest areas has been broadly documented and represents the main cause of deforestation that has occurred for the last decades. Such reality is not different in indigenous lands, and has been considered as an important obstacle for individuals who directly depend upon the appropriate management of natural resources to maintain their traditions. We investigated the seed rain, seed bank and natural regeneration of native woody species within a degraded pasture land in different distances from an adjacent seasonal semideciduous forest fragment to define methodological procedures based on ecological processes that might subsidize forest restoration in an indigenous land. Most seeds and seedlings picked from the seed rain and seed bank belonged to anemochoric and autochoric dispersing shrubby and herbaceous species originated in the pasture land. The woody species regeneration, on the other hand, reached higher levels, in terms of abundance and richness, as the forest fragment became closer. Zoochoric dispersal was predominant among such species and was mainly detected closer to the forest fragment. Several woody species picked in the forest fragment were also found in the pasture land, thus reinforcing their important role in supplying propagules and easing the successional process. (c) 2007 Elsevier B.V. All rights reserved.

Can intensive management accelerate the restoration of Brazil`s Atlantic forests?

Only 7% of the once extensive forest along the eastern coast of Brazil remains, and much of that is degraded and threatened by agricultural expansion and urbanization. We wondered if methods similar to those developed to establish fast-growing Eucalyptus plantations might also work to enhance survival and growth of rainforest species on degraded pastures composed of highly competitive C(4) grasses. An 8-factor experiment was laid out to contrast the value of different intensities of cultivation, application of fertilizer and weed control on the growth and survival of a mixture of 20 rainforest species planted at two densities: 3 m x 1 m, and 3 m x 2 m. Intensive management increased seedling survival from 90% to 98%, stemwood production and leaf area index (LAI) by similar to 4-fold, and stemwood production per unit of light absorbed by 30%. Annual growth in stem biomass was closely related to LAI alone (r(2) = 0.93, p < 0.0001), and the regression improved further in combination with canopy nitrogen content (r(2) =0.99, p < 0.0001). Intensive management resulted in a nearly closed forest canopy in less than 4 years, and offers a practical means to establish functional forests on abandoned agricultural land. (C) 2009 Elsevier B.V. All rights reserved.

Seed development, yield and quality of two palm species growing in different tropical forest types in SE Brazil: implications for ecological restoration

Natural forest remnants have been set as seed production fields to supply seeds of native tree species for tropical forest restoration, but the effect of different forest types on seed production has not been accessed to date for palm species. In this work, we studied seed development, yield, and quality of two palm species in different tropical forest types in SE Brazil. Seed production of palmiteiro (Euterpe edulis) and queen-palm (Syagrus romanzoffiana), which are largely used in restoration efforts due to their importance for vertebrate frugivores, were studied in natural remnants of Atlantic Rainforest, Restinga Forest, Seasonally Dry Forest, and Cerrado Forest. We studied seed development, yield, size, and germination of seed lots produced in some of these forest types, including seeds harvested in 2008, 2009, and both years. Seed yield and quality, as well as seed dry mass in 2009, were higher for palmiteiro seeds produced in the Atlantic Rainforest, while queen-palm seeds produced at the Restinga Forest showed the higher mass and yield, but the lowest physiological potential. Consequently, these natural differences of seed yield and quality have to be taken into account for establishing standards for seed commercialization and analysis, seed pricing, and seedling production in forest nurseries.

Large-scale ecological restoration of high-diversity tropical forests in SE Brazil

The complex interactions among endangered ecosystems, landowners` interests, and different models of land tenure and use, constitute an important series of challenges for those seeking to maintain and restore biodiversity and augment the flow of ecosystem services. Over the past 10 years, we have developed a data-based approach to address these challenges and to achieve medium and large-scale ecological restoration of riparian areas on private lands in the state of Sao Paulo, southeastern Brazil. Given varying motivations for ecological restoration, the location of riparian areas within landholdings, environmental zoning of different riparian areas, and best-practice restoration methods were developed for each situation. A total of 32 ongoing projects, covering 527,982 ha, were evaluated in large sugarcane farms and small mixed farms, and six different restoration techniques have been developed to help upscale the effort. Small mixed farms had higher portions of land requiring protection as riparian areas (13.3%), and lower forest cover of riparian areas (18.3%), than large sugarcane farms (10.0% and 36.9%, respectively for riparian areas and forest cover values). In both types of farms, forest fragments required some degree of restoration. Historical anthropogenic degradation has compromised forest ecosystem structure and functioning, despite their high-diversity of native tree and shrub species. Notably, land use patterns in riparian areas differed markedly. Large sugarcane farms had higher portions of riparian areas occupied by highly mechanized agriculture, abandoned fields, and anthropogenic wet fields created by siltation in water courses. In contrast, in small mixed crop farms, low or non-mechanized agriculture and pasturelands were predominant. Despite these differences, plantations of native tree species covering the entire area was by far the main restoration method needed both by large sugarcane farms (76.0%) and small mixed farms (92.4%), in view of the low resilience of target sites, reduced forest cover, and high fragmentation, all of which limit the potential for autogenic restoration. We propose that plantations should be carried out with a high-diversity of native species in order to create biologically viable restored forests, and to assist long-term biodiversity persistence at the landscape scale. Finally, we propose strategies to integrate the political, socio-economic and methodological aspects needed to upscale restoration efforts in tropical forest regions throughout Latin America and elsewhere. (C) 2010 Elsevier BA/. All rights reserved.

Restoration of Pattern Recognition Receptor Costimulation to Treat Chromoblastomycosis, a Chronic Fungal Infection of the Skin

Chromoblastomycosis is a chronic skin infection caused by the fungus Fonsecaea pedrosoi. Exploring the reasons underlying the chronic nature of F. pedrosoi infection in a murine model of chromoblastomycosis, we find that chronicity develops due to a lack of pattern recognition receptor (PRR) costimulation. F. pedrosoi was recognized primarily by C-type lectin receptors (CLRs), but not by Toll-like receptors (TLRs), which resulted in the defective induction of proinflammatory cytokines. Inflammatory responses to F. pedrosoi could be reinstated by TLR costimulation, but also required the CLR Mincle and signaling via the Syk/CARD9 pathway. Importantly, exogenously administering TLR ligands helped clear F. pedrosoi infection in vivo. These results demonstrate how a failure in innate recognition can result in chronic infection, highlight the importance of coordinated PRR signaling, and provide proof of the principle that exogenously applied PRR agonists can be used therapeutically.

PHRENIC NERVE TRANSFER IN THE RESTORATION OF ELBOW FLEXION IN BRACHIAL PLEXUS AVULSION INJURIES: HOW EFFECTIVE AND SAFE IS IT?

OBJECTIVE: Phrenic nerve transfer has been used for treating lesions of the brachial plexus since 1970. Although, today, surgeons are more experienced with the technique, there are still widespread concerns about its effects on pulmonary function. This study was undertaken to evaluate the effectiveness and safety of this procedure. METHODS: Fourteen patients with complete palsy of the upper limb were submitted to phrenic nerve transfer as part of a strategy for surgical reconstruction of their plexuses. Two patients were lost to follow-up, and 2 patients were followed for less than 2 years. Of the remaining 10 patients, 9 (90%) were male. The lesions affected both sides equally. The mean age of the patients was 24.8 years (range, 14-43 years), and the mean interval from injury to surgery was 6 months (range, 3-9 months). The phrenic nerve was always transferred to the musculocutaneous nerve, and a nerve graft (mean length, 8 cm; range, 4.5-12 cm) was necessary in all cases. RESULTS: There was no major complication related to the surgery. Seven patients (70%) recovered functional level biceps strength (Medical Research Council grade >= 3). All of the patients exhibited a transient decrease in pulmonary function tests, but without clinical respiratory problems. CONCLUSION: On the basis of our small series and data from the literature, we conclude that phrenic nerve transfer in well-selected patients is a safe and effective procedure for recovering biceps function.