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.

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.

Ocklawaha River restoration : the fate of the Rodman Reservoir

The Rodman Reservoir, an impoundment on the Ocklawaha River in north central Florida, is a last remnant of the Cross-Florida Barge Canal (CFBC). The canal, conceived in the 1820's, was designed by the U.S. Army Corps of Engineers (USACE) to shorten shipping lanes between the Fulf ports and the Atlantic coast. Opposition to CFBC by Florida's young environmental movement led to a half in construction of the CFBC in 1971, but decommissioning of the already-constructed Rodman dam and the reservoir behind it has been mired in controversy every since.

Inexact uniformization method for computing transient distributions of Markov chains

The uniformization method (also known as randomization) is a numerically stable algorithm for computing transient distributions of a continuous time Markov chain. When the solution is needed after a long run or when the convergence is slow, the uniformization method involves a large number of matrix-vector products. Despite this, the method remains very popular due to its ease of implementation and its reliability in many practical circumstances. Because calculating the matrix-vector product is the most time-consuming part of the method, overall efficiency in solving large-scale problems can be significantly enhanced if the matrix-vector product is made more economical. In this paper, we incorporate a new relaxation strategy into the uniformization method to compute the matrix-vector products only approximately. We analyze the error introduced by these inexact matrix-vector products and discuss strategies for refining the accuracy of the relaxation while reducing the execution cost. Numerical experiments drawn from computer systems and biological systems are given to show that significant computational savings are achieved in practical applications.

Terra Preta : bioenergy, soil restoration, urban agriculture, art algorithm

The 2010 LAGI competition was held on three underutilized sites in the United Arab Emirates. By choosing Staten Island, New York in 2012 the competition organises have again brought into question new roles for public open space in the contemporary city. In the case of the UEA sites, the competition produced many entries which aimed to create a sculpture and by doing so, they attracted people to the selected empty spaces in an arid climate. In a way these proposals were the incubators and the new characters of these empty spaces. The competition was thus successful at advancing understandings of the expanded role of public open spaces in EAU and elsewhere. LAGI 2012 differs significantly to the UAE program because Fresh Kills Park has already been planned as a public open space for New Yorkers - with or without these clean energy sculptures. Furthermore, Fresh Kills Park is already an (gas) energy generating site in its own right. We believe Fresh Kills Park, as a site, presents a problem which somewhat transcends the aims of the competition brief. Advancing a sustainable urban design proposition for the site therefore requires a fundamental reconsideration of the established paradigms public open space. Hence our strategy is to not only create an energy generating, site specific art work, but to create synergy between the public and the site engagement while at the same time complement the idiosyncrasies of the pre-existing engineered landscape. Current PhD research about energy generation in public open spaces informs this work.

Restoration of native folding of single-stranded DNA sequences through reverse mutations: an indication of a new epigenetic mechanism

We used in vivo (biological), in silico (computational structure prediction), and in vitro (model sequence folding) analyses of single-stranded DNA sequences to show that nucleic acid folding conservation is the selective principle behind a high-frequency single-nucleotide reversion observed in a three-nucleotide mutated motif of the Maize streak virus replication associated protein (Rep) gene. In silico and in vitro studies showed that the three-nucleotide mutation adversely affected Rep nucleic acid folding, and that the single-nucleotide reversion [C(601)A] restored wild-type-like folding. In vivo support came from infecting maize with mutant viruses: those with Rep genes containing nucleotide changes predicted to restore a wild-type-like fold [A(601)/G(601)] preferentially accumulated over those predicted to fold differently [C(601)/T(601)], which frequently reverted to A(601) and displaced the original population. We propose that the selection of native nucleic acid folding is an epigenetic effect, which might have broad implications in the evolution of plants and their viruses.

A wide area monitoring system based load restoration method

Restoring a large-scale power system has always been a complicated and important issue. A lot of research work has been done on different aspects of the whole power system restoration procedure. However, more time will be required to complete the power system restoration process in an actual situation if accurate and real-time system data cannot be obtained. With the development of the wide area monitoring system (WAMS), power system operators are capable of accessing to more accurate data in the restoration stage after a major outage. The ultimate goal of the system restoration is to restore as much load as possible while in the shortest period of time after a blackout, and the restorable load can be estimated by employing WAMS. Moreover, discrete restorable loads are employed considering the limited number of circuit-breaker operations and the practical topology of distribution systems. In this work, a restorable load estimation method is proposed employing WAMS data after the network frame has been reenergized, and WAMS is also employed to monitor the system parameters in case the newly recovered system becomes unstable again. The proposed method has been validated with the New England 39-Bus system and an actual power system in Guangzhou, China.

Re-strengthening 20th century architectural heritage : A case study of Brisbane City Hall restoration

Restoring old buildings to conform the current building policies and standards is a great challenge to engineers and architects. The restoration of the Brisbane City Hall, a heritage building listed by the State of Queensland in Australia, developed an innovative approach to upgrade the building using the method called ‘concrete overlay’ following the guidelines of both the International Council on Monuments and Sites and the Burra Charter of Australia. Concrete overlay is a new method of structural strengthening by drilling new reinforcement and placing new concrete on top of the existing structure, akin to a bone transplant or bone grafting in the case of a human being. This method is popularly used for newer bridges which have suffered load stresses. However, this method had never been used on any heritage buildings which were built on different conditions and standards. The compatibility of this method is currently being monitored. Most of the modern historic buildings are rapidly deteriorating and require immediate interventions in order to be saved. As most of these heritage buildings are on the stage of advanced deterioration, significant attempts are being made and several innovations are being applied to upgrade these structures to conform with the current building requirements. To date, the knowledge and literature in regarding ‘concrete cancer’ in relation to rehabilitating these reinforced concrete heritage structures is significantly lacking. It is hoped that the method of concrete overlay and the case study of Brisbane City Hall restoration will contribute to the development of restoration techniques and policies for Modern Heritage Buildings.