9,793 research outputs found
Personal Papers (MS 80-0002)
No full textLetter from I. H. Kempner to Leslie L. Roos discussing Roos returning to practicing law and his connections with the District Attorney's office in San Francisco
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
What's on a machine's mind? Models for reasoning with incomplete and uncertain knowledge
No full textElectrical Engineering, Mathematics and Computer Scienc
Revue générale des Sciences. — 30 juin. L. Roos et E. Hédon. L’Alcool et sa valeur alimentaire.
No full textRevue générale des Sciences. — 30 juin. L. Roos et E. Hédon. L’Alcool et sa valeur alimentaire.. In: La revue pédagogique, tome 43, Juillet-Décembre 1903. p. 197
Revue générale des Sciences. — 30 juin. L. Roos et E. Hédon. L’Alcool et sa valeur alimentaire.
No full textRevue générale des Sciences. — 30 juin. L. Roos et E. Hédon. L’Alcool et sa valeur alimentaire.. In: La revue pédagogique, tome 43, Juillet-Décembre 1903. p. 197
Joseph Kardinal Höffner, Christliche Gesellschaftslehre. Hrg von L. Roos Kevelaer, 1997
No full textThiel Marie-Jo. Joseph Kardinal Höffner, Christliche Gesellschaftslehre. Hrg von L. Roos Kevelaer, 1997. In: Revue des Sciences Religieuses, tome 74, fascicule 2, 2000. p. 268
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
Quantum chemical calculations show that the uranium molecule U2 has a quintuple bond
No full textCovalent bonding is commonly described by Lewis's theory(1), with an electron pair shared between two atoms constituting one full bond. Beginning with the valence bond description(2) for the hydrogen molecule, quantum chemists have further explored the fundamental nature of the chemical bond for atoms throughout the periodic table, confirming that most molecules are indeed held together by one electron pair for each bond. But more complex binding may occur when large numbers of atomic orbitals can participate in bond formation. Such behaviour is common with transition metals. When involving heavy actinide elements, metal-metal bonds might prove particularly complicated. To date, evidence for actinide-actinide bonds is restricted to the matrix-isolation(3) of uranium hydrides, including H2U-UH2, and the gas-phase detection(4) and preliminary theoretical study(5) of the uranium molecule, U-2. Here we report quantum chemical calculations on U-2, showing that, although the strength of the U-2 bond is comparable to that of other multiple bonds between transition metals, the bonding pattern is unique. We find that the molecule contains three electron-pair bonds and four one-electron bonds (that is, 10 bonding electrons, corresponding to a quintuple bond), and two ferromagnetically coupled electrons localized on one U atom each-so all known covalent bonding types are contributing
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
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