Local convergence of a sequential quadratic programming method for a class of nonsmooth nonconvex objectives

A sequential quadratic programming (SQP) algorithm is designed for nonsmooth optimization problems with upper-C^2 objective functions. Upper-C^2 functions are locally equivalent to difference-of-convex (DC) functions with smooth convex parts. They arise naturally in many applications such as certain classes of solutions to parametric optimization problems, e.g., recourse of stochastic programming, and projection onto closed sets. The proposed algorithm conducts line search and adopts an exact penalty merit function. The potential inconsistency due to the linearization of constraints are addressed through relaxation, similar to that of Sl_1QP. We show that the algorithm is globally convergent under reasonable assumptions. Moreover, we study the local convergence behavior of the algorithm under additional assumptions of Kurdyka-{\L}ojasiewicz (KL) properties, which have been applied to many nonsmooth optimization problems. Due to the nonconvex nature of the problems, a special potential function is used to analyze local convergence. We show that under acceptable assumptions, upper bounds on local convergence can be proven. Additionally, we show that for a large number of optimization problems with upper-C^2 objectives, their corresponding potential functions are indeed KL functions. Numerical experiment is performed with a power grid optimization problem that is consistent with the assumptions and analysis in this paper

Are we seeing the beginnings of Inflation?

Phantom Cosmology provides an unique opportunity to "connect" the phantom driven (low en- ergy meV scale) dark energy phase to the (high energy GUT scale) inflationary era. This is possible because the energy density increases in phantom cosmology. We present a concrete model where the energy density, but not the scale factor, cycles through phases of standard radiation/matter domi- nation followed by dark energy/inflationary phases, and the pattern repeating itself. An interesting feature of the model is that once we include interactions between the "phantom fluid" and ordinary matter, the Big rip singularity is avoided with the phantom phase naturally giving way to a near exponential inflationary expansion.Comment: 17 pages, 1 figur

The role of reactive astrocitose in the chronological evolution of traumatic brain injury

Introduction and objectives. This study aims to investigate whether the cerebral modifications of posttraumatic reactive astrocitose can be considered an objective criterion for determining the age of traumatic cranio-cerebral lesions. Materials and methods. The present study consists of a series of 23 medico-legal cases that underwent autopsy inTeleormanCounty(Romania) Department of Forensic Medicine during 2007–2016, with full immune-histochemical microscopic examination using GFAP staining. The study consists of two groups, a series of 13 cases with cranio-cerebral trauma with different posttraumatic survival periods and 9 cases as a control group. Results and discussions. We discovered GFAP+ reactive astrocytes even when death occurred immediately after the trauma event and up to 4 months after the traumatic incident. We also discovered an intense positive correlation between the density of the GFAP+ cell from the perilesional area and the posttraumatic survival period. The highest cerebral density of the GFAP+ astrocytes occurred with acute death prior (1 to 24 hours) and the lowest in the chronic period (over 2 weeks). Conclusions. The gradual and differentiated appearance of the reactive astrocytes in close relation with the cerebral posttraumatic interval, with specific lesional and perilesional distribution as well as in surrounding area, clearly demonstrates that the state of the reactive astrocitose may constitute an objective index for evaluation of the elapsed time after the posttraumatic event

Returns Management for Time-sensitive Products: What is the Value of RFID and Sensor Technologies?

This contribution concerns itself with the value of RFID and sensor technologies to reverse logistics processes. Our research is motivated by the question, to what extent the accuracy of information on product quality delivered by such technologies impacts the total recovered value companies obtain from returned goods in an industry with time-sensitive products. For this purpose, we first present a case study to examine the returns management process at a manufacturer of high-tech consumer electronics. We then develop an analytical model to study the monetary benefits in a scenario with RFID-enabled product disposition. Our results first show that RFID allows for a redesign of the return process which performs more efficiently regarding total recovered value depending on technology costs (i.e. tag costs) and capabilities (i.e. sufficient sensor-delivered parameters to rightly infer the product quality). Second, our results indicate that maximum benefits can be drawn with lower accuracy but early decision on the disposition option

Compressive sensing adaptation for polynomial chaos expansions

Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of the underlying Gaussian germ. Several rotations have been proposed in the literature resulting in adaptations with different convergence properties. In this paper we present a new adaptation mechanism that builds on compressive sensing algorithms, resulting in a reduced polynomial chaos approximation with optimal sparsity. The developed adaptation algorithm consists of a two-step optimization procedure that computes the optimal coefficients and the input projection matrix of a low dimensional chaos expansion with respect to an optimally rotated basis. We demonstrate the attractive features of our algorithm through several numerical examples including the application on Large-Eddy Simulation (LES) calculations of turbulent combustion in a HIFiRE scramjet engine.Comment: Submitted to Journal of Computational Physic

A computer method for moment-curvature analysis of composite steel-concrete cross-sections of arbitrary shape

This paper presents a new computer method for moment-curvature analysis of arbitrary-shaped composite steel-concrete cross-sections that are subjected to biaxial bending and axial force. The complete moment-curvature diagrams are determined such that axial force and bending moment ratio is kept constant. A strain-driven algorithm has been developed, the solution of the nonlinear equilibrium equations is controlled by the assumed strain values in the most compressed point and by solving just two coupled nonlinear equations. Such an approach may be used to assess accurately the main features of the elasto-plastic behaviour of composite cross-sections: multiple yielding points associated to different materials, flexural and axial rigidity, moment-curvature relationship in pre and post-critical domain and curvature ductility detecting also unloaded regions of the cross-sections that may occur even under monotonically increasing of the total bending moment. Since the Jacobian’s of the resulted nonlinear system of equations is always positive definite the convergence stability is not sensitive to the initial/starting values of the iterative process and to the strain softening exhibited by the concrete in compression. By using a path integral technique on boundary of cross-section area, gradual spread of plasticity and residual stress distribution assumed for encased steel elements are accurately considered reducing also the computational time significantly. In order to illustrate the proposed method and its accuracy and efficiency, a computer program has been developed and used to study several representative examples. The numerical studies presented and comparisons made prove the effectiveness and time saving of the proposed method of analysis

Relaxing Cosmological Constraints on Large Extra Dimensions

We reconsider cosmological constraints on extra dimension theories from the excess production of Kaluza-Klein gravitons. We point out that, if the normalcy temperature is above 1 GeV, then graviton states produced at this temperature will decay early enough that they do not affect the present day dark matter density, or the diffuse gamma ray background. We rederive the relevant cosmological constraints for this scenario.Comment: 17 pages, latex, revtex4; added a short discussion of other constraints, reference