214 research outputs found
Overlapping Schwarz Decomposition for Constrained Quadratic Programs
We present an overlapping Schwarz decomposition algorithm for constrained
quadratic programs (QPs). Schwarz algorithms have been traditionally used to
solve linear algebra systems arising from partial differential equations, but
we have recently shown that they are also effective at solving structured
optimization problems. In the proposed scheme, we consider QPs whose algebraic
structure can be represented by graphs. The graph domain is partitioned into
overlapping subdomains (yielding a set of coupled subproblems), solutions for
the subproblems are computed in parallel, and convergence is enforced by
updating primal-dual information in the overlapping regions. We show that
convergence is guaranteed if the overlap is sufficiently large and that the
convergence rate improves exponentially with the size of the overlap.
Convergence results rely on a key property of graph-structured problems that is
known as exponential decay of sensitivity. Here, we establish conditions under
which this property holds for constrained QPs (as those found in network
optimization and optimal control), thus extending existing work that addresses
unconstrained QPs. The numerical behavior of the Schwarz scheme is demonstrated
by using a DC optimal power flow problem defined over a network with 9,241
nodes
Combining the regularization strategy and the SQP to solve MPCC - A MATLAB implementation
Mathematical Program with Complementarity Constraints (MPCC) plays a very
important role in many fields such as engineering design, economic equilibrium,
multilevel game, and mathematical programming theory itself. In theory its constraints
fail to satisfy a standard constraint qualification such as the linear independence
constraint qualification (LICQ) or the Mangasarian-Fromovitz constraint
qualification (MFCQ) at any feasible point. As a result, the developed nonlinear
programming theory may not be applied to MPCC class directly. Nowadays, a natural
and popular approach is try to find some suitable approximations of an MPCC
so that it can be solved by solving a sequence of nonlinear programs.
This work aims to solve the MPCC using nonlinear programming techniques,
namely the SQP and the regularization scheme. Some algorithms with two iterative
processes, the inner and the external, were developed. A set of AMPL problems
from MacMPEC database [7] were tested. The algorithms performance comparative
analysis was carried out
A Multifaceted Mathematical Approach for Complex Systems
Applied mathematics has an important role to play in developing the tools needed for the analysis, simulation, and optimization of complex problems. These efforts require the development of the mathematical foundations for scientific discovery, engineering design, and risk analysis based on a sound integrated approach for the understanding of complex systems. However, maximizing the impact of applied mathematics on these challenges requires a novel perspective on approaching the mathematical enterprise. Previous reports that have surveyed the DOE's research needs in applied mathematics have played a key role in defining research directions with the community. Although these reports have had significant impact, accurately assessing current research needs requires an evaluation of today's challenges against the backdrop of recent advances in applied mathematics and computing. To address these needs, the DOE Applied Mathematics Program sponsored a Workshop for Mathematics for the Analysis, Simulation and Optimization of Complex Systems on September 13-14, 2011. The workshop had approximately 50 participants from both the national labs and academia. The goal of the workshop was to identify new research areas in applied mathematics that will complement and enhance the existing DOE ASCR Applied Mathematics Program efforts that are needed to address problems associated with complex systems. This report describes recommendations from the workshop and subsequent analysis of the workshop findings by the organizing committee
An adaptive hierarchical domain decomposition method for parallel contact dynamics simulations of granular materials
A fully parallel version of the contact dynamics (CD) method is presented in
this paper. For large enough systems, 100% efficiency has been demonstrated for
up to 256 processors using a hierarchical domain decomposition with dynamic
load balancing. The iterative scheme to calculate the contact forces is left
domain-wise sequential, with data exchange after each iteration step, which
ensures its stability. The number of additional iterations required for
convergence by the partially parallel updates at the domain boundaries becomes
negligible with increasing number of particles, which allows for an effective
parallelization. Compared to the sequential implementation, we found no
influence of the parallelization on simulation results.Comment: 19 pages, 15 figures, published in Journal of Computational Physics
(2011
DejaVu: Intra-operative Simulation for Surgical Gesture Rehearsal
International audienceAdvances in surgical simulation and surgical augmented reality have changed the way surgeons prepare for practice and conduct medical procedures. Despite considerable interest from surgeons, the use of simulation is still predominantly confined to pre-operative training of surgical tasks and the lack of robustness of surgical augmented reality means that it is seldom used for surgical guidance. In this paper, we present DejaVu, a novel surgical simulation approach for intra-operative surgical gesture rehearsal. With DejaVu we aim at bridging the gap between pre-operative surgical simulation and crucial but not yet robust intra-operative surgical augmented reality. By exploiting intra-operative images we produce a simulation that faithfully matches the actual procedure without visual discrepancies and with an underlying physical modelling that performs real-time deformation of organs and surrounding tissues, surgeons can interact with the targeted organs through grasping, pulling or cutting to immediately rehearse their next gesture. We present results on different in vivo surgical procedures and demonstrate the feasibility of practical use of our system
The use of Artificial Neural Networks to estimate seismic damage and derive vulnerability functions for traditional masonry
This paper discusses the adoption of Artificial Intelligence-based techniques to estimate seismic damage, not with the goal of replacing existing approaches, but as a mean to improve the precision of empirical methods. For such, damage data collected in the aftermath of the 1998 Azores earthquake (Portugal) is used to develop a comparative analysis between damage grades obtained resorting to a classic damage formulation and an innovative approach based on Artificial Neural Networks (ANNs). The analysis is carried out on the basis of a vulnerability index computed with a hybrid seismic vulnerability assessment methodology, which is subsequently used as input to both approaches. The results obtained are then compared with real post-earthquake damage observation and critically discussed taking into account the level of adjustment achieved by each approach. Finally, a computer routine that uses the ANN as an approximation function is developed and applied to derive a new vulnerability curve expression. In general terms, the ANN developed in this study allowed to obtain much better approximations than those achieved with the original vulnerability approach, which has revealed to be quite non-conservative. Similarly, the proposed vulnerability curve expression was found to provide a more accurate damage prediction than the traditional analytical expressions.SFRH/BPD/122598/2016info:eu-repo/semantics/publishedVersio
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