On affine scaling inexact dogleg methods for bound-constrained nonlinear systems

Within the framework of affine scaling trust-region methods for bound constrained problems, we discuss the use of a inexact dogleg method as a tool for simultaneously handling the trust-region and the bound constraints while seeking for an approximate minimizer of the model. Focusing on bound-constrained systems of nonlinear equations, an inexact affine scaling method for large scale problems, employing the inexact dogleg procedure, is described. Global convergence results are established without any Lipschitz assumption on the Jacobian matrix, and locally fast convergence is shown under standard assumptions. Convergence analysis is performed without specifying the scaling matrix used to handle the bounds, and a rather general class of scaling matrices is allowed in actual algorithms. Numerical results showing the performance of the method are also given

Adaptive Regularization Algorithms with Inexact Evaluations for Nonconvex Optimization

A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that is constraints whose evaluation and enforcement has negligible cost) under the assumption that the derivative of highest degree is $\beta$-H\"{o}lder continuous. It features a very flexible adaptive mechanism for determining the inexactness which is allowed, at each iteration, when computing objective function values and derivatives. The complexity analysis covers arbitrary optimality order and arbitrary degree of available approximate derivatives. It extends results of Cartis, Gould and Toint (2018) on the evaluation complexity to the inexact case: if a $q$th order minimizer is sought using approximations to the first $p$ derivatives, it is proved that a suitable approximate minimizer within $\epsilon$ is computed by the proposed algorithm in at most $O(\epsilon^{-\frac{p+\beta}{p-q+\beta}})$ iterations and at most $O(|\log(\epsilon)|\epsilon^{-\frac{p+\beta}{p-q+\beta}})$ approximate evaluations. An algorithmic variant, although more rigid in practice, can be proved to find such an approximate minimizer in $O(|\log(\epsilon)|+\epsilon^{-\frac{p+\beta}{p-q+\beta}})$ evaluations.While the proposed framework remains so far conceptual for high degrees and orders, it is shown to yield simple and computationally realistic inexact methods when specialized to the unconstrained and bound-constrained first- and second-order cases. The deterministic complexity results are finally extended to the stochastic context, yielding adaptive sample-size rules for subsampling methods typical of machine learning.Comment: 32 page

Adaptive Regularization for Nonconvex Optimization Using Inexact Function Values and Randomly Perturbed Derivatives

A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function with Lipschitz continuous $p$-th derivative and given an arbitrary optimality order $q \leq p$, it is shown that this algorithm will, in expectation, compute such a point in at most $O\left(\left(\min_{j\in\{1,\ldots,q\}}\epsilon_j\right)^{-\frac{p+1}{p-q+1}}\right)$ inexact evaluations of $f$ and its derivatives whenever $q\in\{1,2\}$, where $\epsilon_j$ is the tolerance for $j$th order accuracy. This bound becomes at most $O\left(\left(\min_{j\in\{1,\ldots,q\}}\epsilon_j\right)^{-\frac{q(p+1)}{p}}\right)$ inexact evaluations if $q>2$ and all derivatives are Lipschitz continuous. Moreover these bounds are sharp in the order of the accuracy tolerances. An extension to convexly constrained problems is also outlined.Comment: 22 page

IMAGE ORIENTATION WITH A HYBRID PIPELINE ROBUST TO ROTATIONS AND WIDE-BASELINES

The extraction of reliable and repeatable interest points among images is a fundamental step for automatic image orientation (Structure-From-Motion). Despite recent progresses, open issues in challenging conditions - such as wide baselines and strong light variations - are still present. Over the years, traditional hand-crafted methods have been paired by learning-based approaches, progressively updating the state-of-the-art according to recent benchmarks. Notwithstanding these advancements, learning-based methods are often not suitable for real photogrammetric surveys due to their lack of rotation invariance, a fundamental requirement for these specific applications. This paper proposes a novel hybrid image matching pipeline which employs both hand-crafted and deep-based components, to extract reliable rotational invariant keypoints optimized for wide-baseline scenarios. The proposed hybrid pipeline was compared with other hand-crafted and learning-based state-of-the-art approaches on some photogrammetric datasets using metric ground-truth data. Results show that the proposed hybrid matching pipeline has high accuracy and appeared to be the only method among the evaluated ones able to register images in the most challenging wide-baseline scenarios

An optimally fast objective-function-free minimization algorithm using random subspaces

An algorithm for unconstrained non-convex optimization is described, which does not evaluate the objective function and in which minimization is carried out, at each iteration, within a randomly selected subspace. It is shown that this random approximation technique does not affect the method's convergence nor its evaluation complexity for the search of an $\epsilon$-approximate first-order critical point, which is $\mathcal{O}(\epsilon^{-(p+1)/p})$, where $p$ is the order of derivatives used. A variant of the algorithm using approximate Hessian matrices is also analyzed and shown to require at most $\mathcal{O}(\epsilon^{-2})$ evaluations. Preliminary numerical tests show that the random-subspace technique can significantly improve performance on some problems, albeit, unsurprisingly, not for all.Comment: 23 page

Survival rate of indirectly bonded brackets using single vs. two-component orthodontic adhesive: A 12-month split-mouth clinical trial

Objective: Compare the bonding survival rate of two distinct bonding materials: Ortho Solo + Gradia LoFlo Resin and single component GC Ortho Connect. Materials and Methods: Indirect bonding fixed appliance treatment was required for 26 consecutive patients, 8 males and 18 females, with a mean age of 22.1 +/- 4.2 years. All patients were treated with SWM (Straight-Wire Mirabella) technique (Sweden and Martina, Due Carrare, Padova, Italy). Each patient's bonding process followed a contralateral pattern. Firstly, a 37 % orthophosphoric acid etching gel was used for 20 s, subsequently the single or two components light-cured adhesives were applied through a split-mouth cross-arch procedure. The patients underwent a 12-month follow-up period and brackets failures were rebounded, but not further included in the study. Statistical analysis was performed to analyse the survival rate of the bonding materials and the influence of the variables, with a significant level of α = 0,05. Results: The GC Connect group was used on 349 teeth, while the Ortho Solo + Gradia group was used on 351 teeth, and the indirect debonding rate was respectively 17.5% and 12.8%. With respect to the total sample, statistically significant values were found for both sex and dental arch. The bracket's survival rate for incisors, canines, premolars and molars was not significant. However, a higher debonding rate was clinically appreciable in upper and lower molars. Conclusion: In a 12-months observation period, considering all maxillary and mandibular teeth the indirect survival rate for the group GC Ortho Connect and Ortho Solo + Gradia was respectively 82.5% and 87.2%. Although the difference was not significant, a pronounced tendency to debonding for the single component group was appreciable from a clinically point of view

The Effect of Thermal Stresses on the Electrical Resistance of Crimped Connections

Cables headed with crimped lugs are frequently used in test laboratories in temperature rise tests carried out to validate electrical devices. The increase in the electrical resistance of the crimped connections can cause high dissipation of power and heat during these tests, impairing their outcome. This work evaluates the effect of thermal stresses on the resistance and on the dissipated power of crimped connections. This resistance was found to be more sensitive to thermal stresses than to mechanical ones analysed in a previous work. A limit of the dissipated power from crimped connections during temperature rise tests was estimated to be about 4 W corresponding to a crimp resistance of 24 mu ohm for tests made at 400 A. Respecting these limits could avoid unnecessary rejections of equipment under test

Role and importance of polymorphisms with respect to DNA methylation for the expression of CYP2E1 enzyme

Different individuals possess slightly different genetic information and show genetically-determined differences in several enzyme activities due to genetic variability. Following an integrated approach,we studied the polymorphisms andmethylation of sites contained in the 5′ flanking region of themetabolizing enzyme CYP2E1 in correlation to its expression in both tumor and non-neoplastic liver cell lines, since to date little is known about the influence of these (epi)genetic elements in basal conditions and under induction by the specific inductor and a demethylating agent. In treated cells, reduced DNA methylation, assessed both at genomic and gene level, was not consistently associatedwith the increase of enzyme expression. Interestingly, the Rsa/Pst haplotype differentially influenced CYP2E1 enzyme expression. In addition, regarding the Variable Number of Tandem Repeats polymorphism, cells with A4/A4 genotype showed a greater expression inhibition (ranging from 20% to 30%) compared with others carrying the A2/A2 one, while those cells bringing A2/A3 genotype showed an increase of expression (of 25%, about). Finally, we demonstrated for the first time that the A2 and A3 CYP2E1 alleles play a more important role in the expression of the enzyme, compared with other (epi)genetic factors, since they are binding sites for trans-acting proteins