Hidden Convexity in Partially Separable Optimization

The paper identifies classes of nonconvex optimization problems whose convex relaxations have optimal solutions which at the same time are global optimal solutions of the original nonconvex problems. Such a hidden convexity property was so far limited to quadratically constrained quadratic problems with one or two constraints. We extend it here to problems with some partial separable structure. Among other things, the new hidden convexity results open up the possibility to solve multi-stage robust optimization problems using certain nonlinear decision rules.convex relaxation of nonconvex problems;hidden convexity;partially separable functions;robust optimization

Environmental sensitivity of n-i-n and undoped single GaN nanowire photodetectors

In this work, we compare the photodetector performance of single defect-free undoped and n-in GaN nanowires (NWs). In vacuum, undoped NWs present a responsivity increment, nonlinearities and persistent photoconductivity effects (~ 100 s). Their unpinned Fermi level at the m-plane NW sidewalls enhances the surface states role in the photodetection dynamics. Air adsorbed oxygen accelerates the carrier dynamics at the price of reducing the photoresponse. In contrast, in n-i-n NWs, the Fermi level pinning at the contact regions limits the photoinduced sweep of the surface band bending, and hence reduces the environment sensitivity and prevents persistent effects even in vacuum

Why Methods for Optimization Problems with Time-Consuming Function Evaluations and Integer Variables Should Use Global Approximation Models

This paper advocates the use of methods based on global approximation models for optimization problems with time-consuming function evaluations and integer variables.We show that methods based on local approximations may lead to the integer rounding of the optimal solution of the continuous problem, and even to worse solutions.Then we discuss a method based on global approximations.Test results show that such a method performs well, both for theoretical and practical examples, without suffering the disadvantages of methods based on local approximations.approximation models;black-box optimization;integer optimization

Hidden Convexity in Partially Separable Optimization

The paper identifies classes of nonconvex optimization problems whose convex relaxations have optimal solutions which at the same time are global optimal solutions of the original nonconvex problems. Such a hidden convexity property was so far limited to quadratically constrained quadratic problems with one or two constraints. We extend it here to problems with some partial separable structure. Among other things, the new hidden convexity results open up the possibility to solve multi-stage robust optimization problems using certain nonlinear decision rules.

An Impulse Control Approach to Dike Height Optimization (Revised version of CentER DP 2011-097)

Abstract: This paper determines the optimal timing of dike heightenings as well as the corresponding optimal dike heightenings to protect against floods. To derive the optimal policy we design an algorithm based on the Impulse Control Maximum Principle. In this way the paper presents one of the first real life applications of the Impulse Control Maximum Principle developed by Blaquiere. We show that the proposed Impulse Control approach performs better than Dynamic Programming with respect to computational time. This is caused by the fact that Impulse Control does not need discretization in time.

Magnetic and Thermodynamic Properties of the Collective Paramagnet-Spin Liquid Pyrochlore Tb2Ti2O7

In a recent letter [Phys. Rev. Lett. {\bf 82}, 1012 (1999)] it was found that the Tb$^{3+}$ magnetic moments in the Tb$_2$Ti$_2$O$_7$ pyrochlore lattice of corner-sharing tetrahedra remain in a {\it collective paramagnetic} state down to 70mK. In this paper we present results from d.c. magnetic susceptibility, specific heat data, inelastic neutron scattering measurements, and crystal field calculations that strongly suggest that (1) the Tb$^{3+}$ ions in Tb$_2$Ti$_2$O$_7$ possess a moment of approximatively 5$\mu_{\rm B}$, and (2) the ground state $g-$tensor is extremely anisotropic below a temperature of $O(10^0)$K, with Ising-like Tb$^{3+}$ magnetic moments confined to point along a local cubic $$diagonal (e.g. towards the middle of the tetrahedron). Such a very large easy-axis Ising like anisotropy along a$$ direction dramatically reduces the frustration otherwise present in a Heisenberg pyrochlore antiferromagnet. The results presented herein underpin the conceptual difficulty in understanding the microscopic mechanism(s) responsible for Tb$_2$Ti$_2$O$_7$ failing to develop long-range order at a temperature of the order of the paramagnetic Curie-Weiss temperature $\theta_{\rm CW} \approx -10^1$K. We suggest that dipolar interactions and extra perturbative exchange coupling(s)beyond nearest-neighbors may be responsible for the lack of ordering of Tb$_2$Ti$_2$O$_7$.Comment: 8 POSTSCRIPT figures included. Submitted to Physical Review B. Contact: [email protected]

Robust optimization of dose-volume metrics for prostate HDR-brachytherapy incorporating target and OAR volume delineation uncertainties

In radiation therapy planning, uncertainties in the definition of the target volume yield a risk of underdosing the tumor. The traditional corrective action in the context of external beam radiotherapy (EBRT) expands the clinical target volume (CTV) with an isotropic margin to obtain the planning target volume (PTV). However, the EBRT-based PTV concept is not directly applicable to brachytherapy (BT) since it can lead to undesirable dose escalation. Here, we present a treatment plan optimization model that uses worst-case robust optimization to account for delineation uncertainties in interstitial high-dose-rate BT of the prostate. A scenario-based method was developed that handles uncertainties in index sets. Heuristics were included to reduce the calculation times to acceptable proportions. The approach was extended to account for delineation uncertainties of an organ at risk (OAR) as well. The method was applied on data from prostate cancer patients and evaluated in terms of commonly used dosimetric performance criteria for the CTV and relevant OARs. The robust optimization approach was compared against the classical PTV margin concept and against a scenario-based CTV margin approach. The results show that the scenario-based margin and the robust optimization method are capable of reducing the risk of underdosage to the tumor. As expected, the scenario-based CTV margin approach leads to dose escalation within the target, whereas this can be prevented with the robust model. For cases where rectum sparing was a binding restriction, including uncertainties in rectum delineation in the planning model led to a reduced risk of a rectum overdose, and in some cases, to reduced target coverage

Long Range Order at Low Temperature in Dipolar Spin Ice

Recently it has been suggested that long range magnetic dipolar interactions are responsible for spin ice behavior in the Ising pyrochlore magnets ${\rm Dy_{2}Ti_{2}O_{7}}$ and ${\rm Ho_{2}Ti_{2}O_{7}}$. We report here numerical results on the low temperature properties of the dipolar spin ice model, obtained via a new loop algorithm which greatly improves the dynamics at low temperature. We recover the previously reported missing entropy in this model, and find a first order transition to a long range ordered phase with zero total magnetization at very low temperature. We discuss the relevance of these results to ${\rm Dy_{2}Ti_{2}O_{7}}$ and ${\rm Ho_{2}Ti_{2}O_{7}}$.Comment: New version of the manuscript. Now contains 3 POSTSCRIPT figures as opposed to 2 figures. Manuscript contains a more detailed discussion of the (i) nature of long-range ordered ground state, (ii) finite-size scaling results of the 1st order transition into the ground state. Order of authors has been changed. Resubmitted to Physical Review Letters Contact: [email protected]