Interior point methods (IPM) rely on the Newton method for solving systems of nonlinear equations. Solving the linear systems which arise from this approach is the most computationally expensive task ...of an interior point iteration. If, due to problem’s inner structure, there are special techniques for efficiently solving linear systems, IPMs demonstrate a reduced computing time and are able to solve large scale optimization problems. It is tempting to try to replace the Newton method by quasi-Newton methods. Quasi-Newton approaches to IPMs either are built to approximate the Lagrangian function for nonlinear programming problems or provide an inexpensive preconditioner. In this work we study the impact of using quasi-Newton methods applied directly to the nonlinear system of equations for general quadratic programming problems. The cost of each iteration can be compared to the cost of computing correctors in a usual interior point iteration. Numerical experiments show that the new approach is able to reduce the overall number of matrix factorizations.
Given a fixed set of identical or different-sized circular items, the problem we deal with consists on finding the smallest object within which the items can be packed. Circular, triangular, squared, ...rectangular and also strip objects are considered. Moreover, 2D and 3D problems are treated. Twice-differentiable models for all these problems are presented. A strategy to reduce the complexity of evaluating the models is employed and, as a consequence, instances with a large number of items can be considered. Numerical experiments show the flexibility and reliability of the new unified approach.
We present a study of Spread F occurrence over a location under the southern crest of the equatorial ionization anomaly (Cachoeira Paulista 22.7°S, 45.0°W, mag. Lat.: 16°S, dip angle: −32.3°, Brazil) ...during the last solar cycle, which presented an extended solar minimum activity. After analyzing hundreds of ionograms obtained with a digital ionosonde DGS 256, between 2001 and 2010, we verified high Spread F occurrence around midnight‐postmidnight during June solstice (Southern Hemisphere winter) with a peak occurrence between 2006 and 2009, when the solar flux has reached very low values (<70 SFU). At the Brazilian sector the occurrence of Spread F is known to be associated with equatorial plasma bubbles (EPBs) and is observed mainly between September and March. On the other hand, EPBs are rarely observed over Cachoeira Paulista (hereafter referred as CP) during June solstice because of the weak magnitudes of the equatorial electric field prereversal enhancement, an essential condition to the development of the large‐scale irregularities at the equatorial region. Despite the rarity of EPBs, we observed several strong Spread F events occurring under low plasma densities conditions which can extend for several hours. We have found evidences that the Spread F events over CP during June solstices of low solar activity can be caused by ionospheric disturbances that are unrelated to equatorial processes. Finally we present a statistical analysis of the events and we suggest that traveling ionospheric disturbances could be one of the main sources of these nonequatorial Spread F events.
Key Points
Spread F
MSTIDs
Solar minimum
The robust adjustment of nonlinear models to data is considered in this paper. When data comes from real experiments, it is possible that measurement errors cause the appearance of discrepant values, ...which should be ignored when adjusting models to them. This work presents a low order-value optimization (LOVO) version of the Levenberg–Marquardt algorithm, which is well suited to deal with outliers in fitting problems. A general algorithm is presented and convergence to stationary points is demonstrated. Numerical results show that the algorithm is successfully able to detect and ignore outliers without too many specific parameters. Parallel and distributed executions of the algorithm are also possible, allowing the use of larger datasets. Comparison against publicly available robust algorithms shows that the present approach is able to find better adjustments in well known statistical models.
The development of Pickering emulsions as ecologically correct stabilized with bio-based material by substituting synthetic petroleum-derived tensoactives assumed a very attractive level, ...representing the current guideline of the global market for homecare industry, food and beverage applications. In this wor, cellulose nanocrystals (CNCs), a hierarchically advanced biomaterial, were produced to stabilize innovative emulsions formulated with western soapberry
Sapindus saponaria
L. oil (SO). Besides, green surfactants (triterpene saponins extracted from
S. saponaria
L. pericarp; SAP) were also investigated to stabilize the oil/water interface. The synergistic combination between cellulose nanowhiskers and the bioactive glycosides has never been reported in the literature. Dynamic interfacial tensions of SAP and SO were firstly investigated, and their capacity to form a plastic membrane at oil/water interface was revealed. Response surface methodology (RSM) was employed to study the influence of the binary systems (CNC:SAP) on the stability of emulsified systems, such as size and zeta potential. In addition, a new calculation was proposed to determine the coverage of the oil droplets formed by the mixture of cellulose crystallites and natural surfactants. The optimal nanoemulsion composition was determined to be 60 w/w (%) of water, 23.905 w/w % of SO, 5 w/w % of CNC and 8.095 w/w% of SAP to produce of smallest droplet (165.1 nm) combined with higher zeta potential module (−46.7 mV). Results highlight the potential of
Sapindus
saponins and cellulose nanowhiskers for efficient producing label-friendly nanoemulsions applicable for drug, cosmeceutical or edible delivery systems.
Graphical abstract
A new method is introduced for solving constrained optimization problems in which the derivatives of the constraints are available but the derivatives of the objective function are not. The method is ...based on the inexact restoration framework, by means of which each iteration is divided in two phases. In the first phase one considers only the constraints, in order to improve feasibility. In the second phase one minimizes a suitable objective function subject to a linear approximation of the constraints. The second phase must be solved using derivative-free methods. An algorithm introduced recently by Kolda, Lewis, and Torczon for linearly constrained derivative-free optimization is employed for this purpose. Under usual assumptions, convergence to stationary points is proved. A computer implementation is described and numerical experiments are presented. PUBLICATION ABSTRACT
Many derivative-free methods for constrained problems are not efficient for minimizing functions on “thin” domains. Other algorithms, like those based on Augmented Lagrangians, deal with thin ...constraints using penalty-like strategies. When the constraints are computationally inexpensive but highly nonlinear, these methods spend many potentially expensive objective function evaluations motivated by the difficulties in improving feasibility. An algorithm that handles this case efficiently is proposed in this paper. The main iteration is split into two steps: restoration and minimization. In the restoration step, the aim is to decrease infeasibility without evaluating the objective function. In the minimization step, the objective function
f
is minimized on a relaxed feasible set. A global minimization result will be proved and computational experiments showing the advantages of this approach will be presented.
In this study we investigate the response of the equatorial F layer to disturbance zonal electric field associated with IMF (interplanetary magnetic field) variations dominated by a strong northward ...Bz episode during the magnetic storm that occurred on 21 January, 2005. We compared the results obtained from Digisondes operated at Fortaleza, Brazil (Geogr. 3.9°S, 38.45°W; dip angle: −11.7°) and Jicamarca, Peru (Geogr. 12.0°S, 76.8°W; dip angle: 0.64°). A large auroral activity (AE) intensification that occurred at ∼1715 UT produced a large F‐layer peak height increase (from 300 km to 600 km) over Jicamarca with no noticeable simultaneous effect over Fortaleza. Then the Bz turning northward at ∼1940 UT with a rapid change in AE that was accompanied by a large decrease of F layer height and total suppression of the PRE over Fortaleza with no simultaneous effect over Jicamarca. Strong increase in the AE index (from ∼400 to 1000 nT) with superimposed oscillations, under Bz North, that soon followed was associated with increases in both the F layer height and the vertical drift velocity over Fortaleza (at 2130 UT), with no corresponding signatures over Jicamarca. These remarkable contrasting responses to prompt penetration electric field (PPEF) as well as to disturbance wind dynamo electric field (DDEF) and other effects observed at the two locations separated only by 2 h in LT in the South American sector are presented and discussed in this paper. Effects onspread‐F development and foF2 behavior during this storm event are also addressed in this work.
Key Points
Prompt penetration eastward electric field under Bz South as well as Bz North
Large contrasts in the storm time response between Fortaleza and Jicamarca
Modulation of the F‐layer by large scale gravity waves
Abstract Quasi-Newton methods are well known techniques for large-scale numerical optimization. They use an approximation of the Hessian in optimization problems or the Jacobian in system of ...nonlinear equations. In the Interior Point context, quasi-Newton algorithms compute low-rank updates of the matrix associated with the Newton systems, instead of computing it from scratch at every iteration. In this work, we show that a simplified quasi-Newton primal-dual interior point algorithm for linear programming, which alternates between Newton and quasi-Newton iterations, enjoys polynomial worst-case iteration complexity. Feasible and infeasible cases of the algorithm are considered and the most common neighborhoods of the central path are analyzed. To the best of our knowledge, this is the first attempt to deliver polynomial worst-case iteration complexity bounds for these methods. Unsurprisingly, the worst-case complexity results obtained when quasi-Newton directions are used are worse than their counterparts when Newton directions are employed. However, quasi-Newton updates are very attractive for large-scale optimization problems where the cost of factorizing the matrices is much higher than the cost of solving linear systems.
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