7,641 research outputs found
Large-Update Infeasible Interior-Point Methods for Linear Optimization
No full textRecently, C. Roos proposed a full-Newton step infeasible interior-point method (IIPM) for linear optimization (LO). Shortly afterwards, Mansouri and Roos presented a variant of this algorithm and Gu et al. a version with a simplified analysis. Roos' algorithm is a path-following method. It uses the so-called homotopy path as a guideline to an optimal solution. The algorithm has the advantage that it uses only full Newton steps (the step size is always 1, hence requires no computation), and its convergence rate is O(n), which coincides with the best known convergence rate for IIPMs. Apart from these nice features, the algorithm has the deficiency that it is a small-update method and hence it is too slow for practical purposes. In this thesis we design a large-update version of Roos' algorithm. We present a practically efficient implementation of (a variant of) the algorithm and compare its performance with that of the well- known LIPSOL package. The numerical results are promising as the iteration numbers of our algorithm are close to those of LIPSOL; in a few cases they outperform LIPSOL. Not surprisingly, as in large-update feasible interior-point methods (FIPMs), there is a gap between the practical and the theoretical behavior of our large-update IIPM. To be more precise, its theoretical convergence rate is O(n?n (log n)³) which is worse than the convergence rate of its full-Newton step variant. This phenomenon is well-known in the field of IPMs, and has been called the irony of IPMs: small-update methods have the best complexity results and are slow in practice, whereas large-update methods have worse complexity results and excellent performance in practice. For example, large-update FIPMs are by a factor worse than that of the full-Newton step FIPMs, i.e., O(?nlogn) versus O(?n). The thesis also contains a survey of IIPMs that have been presented by several authors in last two decades. It covers a wide range of methods, starting from Lustig's algorithm, to the infeasible potential-reduction methods of Mizuno, Kojima and Todd. We focus on convergence properties and polynomiality of the IIPMs presented in our survey.EWIElectrical Engineering, Mathematics and Computer Scienc
Figure 6 in Taxonomic review of the New World tamarins (Primates: Callitrichidae)
No full textFigure 6. The geographical distributions of the tamarins of the mystax group (orange), the oedipus group (purple), and the midas and bicolor groups (green). Map by Stephen D. Nash. © Conservation International.Published as part of Rylands, Anthony B., Heymann, Eckhard W., Alfaro, Jessica Lynch, Buckner, Janet C., Roos, Christian, Matauschek, Christian, Boubli, Jean P., Sampaio, Ricardo & Mittermeier, Russell A., 2016, Taxonomic review of the New World tamarins (Primates: Callitrichidae), pp. 1003-1028 in Zoological Journal of the Linnean Society 177 (4) on page 1014, DOI: 10.1111/zoj.12386, http://zenodo.org/record/536549
Counterexample to a Conjecture on an Infeasible Interior-Point Method
No full textIn [SIAM J. Optim., 16 (2006), pp. 1110–1136], Roos proved that the devised full-step infeasible algorithm has worst-case iteration complexity. This complexity bound depends linearly on a parameter , which is proved to be less than . Based on extensive computational evidence (hundreds of thousands of randomly generated problems), Roos conjectured that (Conjecture 5.1 in the above-mentioned paper), which would yield an iteration full-Newton step infeasible interior-point algorithm. In this paper we present an example showing that is in the order of , the same order as that proved in Roos's original paper. In other words, the conjecture is false.Software TechnologyElectrical Engineering, Mathematics and Computer Scienc
Full-step interior-point methods for symmetric optimization
No full textIn [SIAM J. Optim., 16(4):1110--1136 (electronic), 2006] Roos proposed a full-Newton step Infeasible Interior-Point Method (IIPM) for Linear Optimization (LO). It is a primal-dual homotopy method; it differs from the classical IIPMs in that it uses only full steps. This means that no line searches are needed. In this thesis, we first present an improved full-Newton step IIPM for LO. Then, based on the properties of Euclidean Jordan algebras, we generalize the improved full-Newton step IIPM for LO to full Nesterov-Todd step (NT-step) IIPM for Symmetric Optimization (SO). Since the analysis requires a quadratic convergence result for the feasible case, primal-dual feasible IPMs with full steps are presented as well. Although our devised IIPMs admit the best known iteration bound, from a practical perspective they are not efficient. This is because they always perform according to their worst-case theoretical complexity bounds, which means that only tiny reductions of the so-called barrier parameter are admitted. As a remedy, we propose a more aggressive (adaptive) updating strategy. Finally, our full NT-step IIPM for SO is implemented with both standard and adaptive updates of the barrier parameter. The significant improvement in performance of the adaptive updating strategy over the original short updating strategy is illustrated. The algorithm with adaptive updates is also used to solve problems from the well known library SDPLIB [Optim. Methods Softw., 11/12(1-4):683--690, 1999] of test problems. The results are promising, and to some extend competing with SDPT3 [Math. Program., 95(2, Ser. B):189--217, 2003].Software TechnologyElectrical Engineering, Mathematics and Computer Scienc
The relationship of health/food literacy and salt awareness to daily sodium and potassium intake among a workplace population in Switzerland
No full textBackground and aims: High sodium (Na) and low potassium (K) intake are associated with hypertension and CVD risk. This study explored the associations of health literacy (HL), food literacy (FL), and salt awareness with salt intake, K intake, and Na/K ratio in a workplace intervention trial in Switzerland. Methods and results: The study acquired baseline data from 141 individuals, mean age 44.6 years. Na and K intake were estimated from a single 24-h urine collection. We applied validated instruments to assess HL and FL, and salt awareness. Multiple linear regression was used to investigate the association of explanatory variables with salt intake, K intake, and Na/K. Mean daily salt intake was 8.9 g, K 3.1 g, and Na/K 1.18. Salt intake was associated with sex (p <0.001), and K intake with sex (p <0.001), age (p = 0.02), and waist-to-height ratio (p = 0.03), as was Na/K. HL index and FL score were not significantly associated with salt or K intake but the awareness variable "salt content impacts food/menu choice" was associated with salt intake (p = 0.005). Conclusion: To achieve the established targets for population Na and K intake, health-related knowledge, abilities, and skills related to Na/salt and K intake need to be promoted through combined educational and structural interventions. (C) 2017 The Italian Society of Diabetology, the Italian Society for the Study of Atherosclerosis, the Italian Society of Human Nutrition, and the Department of Clinical Medicine and Surgery, Federico II University. Published by Elsevier B.V.Peer reviewe
Studies on military and foreign policy, political-military gaming
No full textHandwritten on cover "Leslie Roos and Barton Whaley." -- Hand written on t.p., "Leslie Roos." -- Preface lists them as both authors"November 1964.""1528"--handwritten on coverIncludes bibliographical references (p. [48]
Kernel-based interior-point methods for monotone linear complementarity problems over symmetric cones
No full textWe present an interior-point method for monotone linear complementarity problems over symmetric cones (SCLCP) that is based on barrier functions which are defined by a large class of univariate functions, called eligible kernel functions. This class is fairly general and includes the classical logarithmic function, the self-regular functions, as well as many non-self-regular functions as special cases. We provide a unified analysis of the method and give a general scheme on how to calculate the iteration bounds for the entire class. We also calculate the iteration bounds of both large-step and short-step versions of the method for ten frequently used eligible kernel functions. For some of them we match the best known iteration bound for large-step methods, while for short-step methods the best iteration bound is matched for all cases. The paper generalizes results of Lesaja and Roos (SIAM J. Optim. 20(6):3014–3039, 2010) from P ?(?)-LCP over the non-negative orthant to monotone LCPs over symmetric cones.Software Computer TechnologyElectrical Engineering, Mathematics and Computer Scienc
New Primal-dual Interior-point Methods Based on Kernel Functions
No full textTwo important classes of polynomial-time interior-point method (IPMs) are small- and large-update methods, respectively. The theoretical complexity bound for large-update methods is a factor worse than the bound for small-update methods, where denotes the number of (linear) inequalities in the problem. In practice the situation is opposite: implementations of large-update methods are much more efficient than those of small-update methods. This so-called irony of IPMs motivated the present work. Recently J. Peng C. Roos and T. Terlaky were able to design new IPMs with large-updates whose complexity is only a factor worse than for small-update methods. This means that the factor was reduced to , thus significantly reducing the gap between the theoretical behavior of large- and small-update methods. They made use of so-called self-regular barrier (or proximity) functions. Each such barrier function is determined by its (univariate) self-regular kernel function. In these thesis we introduce a new class of kernel functions which differs from the class of self-regular kernel functions. The class is defined by some simple conditions on the kernel function which concern the growth and the barrier behavior of the kernel function. These properties enable us to derive many new and tight estimates that greatly simplify the analysis of IPMs based on these kernel functions. In Chapter 2 we consider ten specific (classes of) kernel functions belonging to the new class, and using the new estimates present a complete complexity analysis for each of these functions. Some of these functions are self-regular and others are not. Iterations bounds both for large- and small-update methods are derived. It is shown that small-update methods based on the new kernel functions all have the same complexity as the classical primal-dual IPM, namely O(\sqrt{n}\,\log\frac{n}{\e}). For large-update methods the best obtained bound is O(\sqrt{n}\,\br{\log n}\,\log\frac{n}{\e}), which is up till now the best known bound for such methods. The results of Chapter 2 for LO are extended to semidefinite optimization in Chapter 3, where we it is shown that at some point the analysis boils down to exactly the same analysis as for the LO case. In Chapter 4 some numerical results are presented. These results show that one of the new kernel functions, with finite barrier term and with the best possible theoretical complexity, performs surprisingly well in our experiments.Electrical Engineering, Mathematics and Computer Scienc
[catalog] Catalogue des tableaux anciens, antiquités et objets d'art, dépendant des collections C..., P. J. Zürcher, Comte Logothète, le faillite de M. W. Greup Gzn.... vente à Amsterdam du 31 mars au 7 avril 1914 ....
No full textBijzondere collectie
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