On the Lipschitz Behavior of Optimal Solutions in Parametric Problems of Quadratic Optimization and Linear Complementarity

In this paper S.M. Robinson's result concerning the upper Lipschitz continuity of polyhedral multifunctions is used to study the Lipschitz behavior of (generally non-polyhedral) optimal set mappings in certain parametric optimization problems. Under mild assumptions, the corresponding value functions are shown to be Lipschitzian on bounded convex sets

Unified aeroacoustics analysis for high speed turboprop aerodynamics and noise. Volume 3: Application of theory for blade loading, wakes, noise, and wing shielding

Results of the program for the generation of a computer prediction code for noise of advanced single rotation, turboprops (prop-fans) such as the SR3 model are presented. The code is based on a linearized theory developed at Hamilton Standard in which aerodynamics and acoustics are treated as a unified process. Both steady and unsteady blade loading are treated. Capabilities include prediction of steady airload distributions and associated aerodynamic performance, unsteady blade pressure response to gust interaction or blade vibration, noise fields associated with thickness and steady and unsteady loading, and wake velocity fields associated with steady loading. The code was developed on the Hamilton Standard IBM computer and has now been installed on the Cray XMP at NASA-Lewis. The work had its genesis in the frequency domain acoustic theory developed at Hamilton Standard in the late 1970s. It was found that the method used for near field noise predictions could be adapted as a lifting surface theory for aerodynamic work via the pressure potential technique that was used for both wings and ducted turbomachinery. In the first realization of the theory for propellers, the blade loading was represented in a quasi-vortex lattice form. This was upgraded to true lifting surface loading. Originally, it was believed that a purely linear approach for both aerodynamics and noise would be adequate. However, two sources of nonlinearity in the steady aerodynamics became apparent and were found to be a significant factor at takeoff conditions. The first is related to the fact that the steady axial induced velocity may be of the same order of magnitude as the flight speed and the second is the formation of leading edge vortices which increases lift and redistribute loading. Discovery and properties of prop-fan leading edge vortices were reported in two papers. The Unified AeroAcoustic Program (UAAP) capabilites are demonstrated and the theory verified by comparison with the predictions with data from tests at NASA-Lewis. Steady aerodyanmic performance, unsteady blade loading, wakes, noise, and wing and boundary layer shielding are examined

Conditions for Optimality and Strong Stability in Nonlinear Programs without assuming Twice Differentiability of Data

The present paper is concerned with optimization problems in which the data are differentiable functions having a continuous or locally Lipschitzian gradient mapping. Its main purpose is to develop second-order sufficient conditions for a stationary solution to a program with C^{1,1} data to be a strict local minimizer or to be a local minimizer which is even strongly stable with respect to certain perturbations of the data. It turns out that some concept of a set-valued directional derivative of a Lipschitzian mapping is a suitable tool to extend well-known results in the case of programs with twice differentiable data to more general situations. The local minimizers being under consideration have to satisfy the Mangasarian-Fromovitz CQ. An application to iterated local minimization is sketched

Entropic approximation for mathematical programs with robust equilibrium constraints

In this paper, we consider a class of mathematical programs with robust equilibrium constraints represented by a system of semi-infinite complementarity constraints (SIC C). We propose a numerical scheme for tackling SICC. Specific ally, by relaxing the complementarity constraints and then randomizing the index set of SICC, we employ the well-known entropic risk measure to approximate the semi-infinite onstraints with a finite number of stochastic inequality constraints. Under some moderate conditions, we quantify the approximation in term s of the feasible set and the optimal value. The approximation scheme is then applied to a class of two stage stochastic mathematical programs with complementarity constraints in combination with the polynomial decision rules. Finally, we extend the discussion to a mathematical program with distributionally robust equilibrium constraints which is essentially a one stage stochastic program with semi-infinite stochastic constraints indexed by some probability measures from an ambiguity set defined through the KL-divergence

Calculus of Tangent Sets and Derivatives of Set Valued Maps under Metric Subregularity Conditions

In this paper we intend to give some calculus rules for tangent sets in the sense of Bouligand and Ursescu, as well as for corresponding derivatives of set-valued maps. Both first and second order objects are envisaged and the assumptions we impose in order to get the calculus are in terms of metric subregularity of the assembly of the initial data. This approach is different from those used in alternative recent papers in literature and allows us to avoid compactness conditions. A special attention is paid for the case of perturbation set-valued maps which appear naturally in optimization problems.Comment: 17 page

The Radius of Metric Subregularity

There is a basic paradigm, called here the radius of well-posedness, which quantifies the "distance" from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often understood as a regularity property, which is usually employed to measure the effect of perturbations and approximations of a problem on its solutions. In this paper we focus on evaluating the radius of the property of metric subregularity which, in contrast to its siblings, metric regularity, strong regularity and strong subregularity, exhibits a more complicated behavior under various perturbations. We consider three kinds of perturbations: by Lipschitz continuous functions, by semismooth functions, and by smooth functions, obtaining different expressions/bounds for the radius of subregularity, which involve generalized derivatives of set-valued mappings. We also obtain different expressions when using either Frobenius or Euclidean norm to measure the radius. As an application, we evaluate the radius of subregularity of a general constraint system. Examples illustrate the theoretical findings.Comment: 20 page

Disagreement in risk groups for metastatic renal cancer.

In patients with metastatic renal cell carcinoma, risk stratification according to the Memorial Sloan-Kettering Cancer Center or the International Metastatic Renal Cell Carcinoma Database Consortium classification systems is a crucial part of clinical assessment and essential for guiding management. New research has now demonstrated that disagreement in risk-group classification is common and prognostically relevant

Concise total syntheses of (–)-jorunnamycin A and (–)-jorumycin enabled by asymmetric catalysis

The bis-tetrahydroisoquinoline (bis-THIQ) natural products have been studied intensively over the past four decades for their exceptionally potent anticancer activity, in addition to strong gram-positive and -negative antibiotic character. Synthetic strategies toward these complex polycyclic compounds have relied heavily on electrophilic aromatic chemistry, such as the Pictet-Spengler reaction, that mimics their biosynthetic pathways. Herein we report an approach to two bis-THIQ natural products, jorunnamycin A and jorumycin, that instead harnesses the power of modern transition-metal catalysis for the three major bond-forming events and proceeds with high efficiency (15 and 16 steps, respectively). By breaking from biomimicry, this strategy allows for the preparation of a more diverse set of non-natural analogs

Outcomes of synchronous and metachronous bilateral small renal masses (< 4 cm):a population‑based cohort study

Objectives: To report longitudinal outcomes of a population based cohort of patients diagnosed with bilateral small renal masses from a period of over 11 years.Patients and Methods: Consecutive patients diagnosed with bilateral small renal masses (synchronous or metachronous) of a defined geographical area were recorded in a large database (TUCAN database) between January 2005 and December 2016. Patients had a unique identifier number and followed during this period using an agreed upon protocol. Clinicopathological characteristics and outcomes of bilateral small renal masses on active surveillance were analysed and compared to propensity score matched sporadic unilateral small renal masses. Data were analysed for renal mass growth rate, rate of intervention and development of metastatic disease and patient survival.Results: A total of 1060 patients were diagnosed with renal cancer, of which bilateral small renal masses accounted for 70 (6.6%) cases. Synchronous SRMs were observed in 63 patients, whereas metachronous lesions were found in seven patients during the study period. Metachronous lesion mean time to appearance was 62 ± 41 months (range, 9 to 149 months). While most cases were sporadic, four were found to be hereditary. Growth rate of bilateral small renal masses did not differ from that of unilateral sporadic small renal masses. Similarly, there were no differences between the groups for rate of interventions and survival.Conclusion: Progression, rate of metastases and survival for patients diagnosed with bilateral small renal masses is similar to those diagnosed with unilateral disease

Epidemiology and screening for renal cancer.

PURPOSE: The widespread use of abdominal imaging has affected the epidemiology of renal cell carcinoma (RCC). Despite this, over 25% of individuals with RCC have evidence of metastases at presentation. Screening for RCC has the potential to downstage the disease. METHODS: We performed a literature review on the epidemiology of RCC and evidence base regarding screening. Furthermore, contemporary RCC epidemiology data was obtained for the United Kingdom and trends in age-standardised rates of incidence and mortality were analysed by annual percentage change statistics and joinpoint regression. RESULTS: The incidence of RCC in the UK increased by 3.1% annually from 1993 through 2014. Urinary dipstick is an inadequate screening tool due to low sensitivity and specificity. It is unlikely that CT would be recommended for population screening due to cost, radiation dose and increased potential for other incidental findings. Screening ultrasound has a sensitivity and specificity of 82-83% and 98-99%, respectively; however, accuracy is dependent on tumour size. No clinically validated urinary nor serum biomarkers have been identified. Major barriers to population screening include the relatively low prevalence of the disease, the potential for false positives and over-diagnosis of slow-growing RCCs. Individual patient risk-stratification based on a combination of risk factors may improve screening efficiency and minimise harms by identifying a group at high risk of RCC. CONCLUSION: The incidence of RCC is increasing. The optimal screening modality and target population remain to be elucidated. An analysis of the benefits and harms of screening for patients and society is warranted