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1.
We consider parametric optimization problems from an algebraic viewpoint. The idea is to find all of the critical points of an objective function thereby determining a global optimum. For generic parameters (data) in the objective function the number of critical points remains constant. This number is known as the algebraic degree of an optimization problem. In this article, we go further by considering the inverse problem of finding parameters of the objective function so it gives rise to critical points exhibiting a special structure. For example if the critical point is in the singular locus, has some symmetry, or satisfies some other algebraic property. Our main result is a theorem describing such parameters.  相似文献   
2.
We consider the problem faced by an online service platform that matches suppliers with consumers. Unlike traditional matching models, which treat them as passive participants, we allow both sides of the market to exercise their choices. To model this setting, we introduce a two-sided assortment optimization model wherein each participant's choice is modeled using a multinomial logit choice function, and the platform's objective is to maximize its expected revenue. We first show that the problem is NP-hard even when the number of suppliers is limited to two and provide a mixed-integer linear programming formulation. Next, we discuss two simple greedy heuristics and argue that these can lead to arbitrarily bad solutions. We then develop relaxations that provide upper and lower bounds and investigate the tightness of these relaxations by obtaining parametric approximation guarantees. Finally, we present numerical results on synthetic data demonstrating the practical utility of these relaxations.  相似文献   
3.
We consider two-stage recourse models with integer restrictions in the second stage. These models are typically non-convex and hence, hard to solve. There exist convex approximations of these models with accompanying error bounds. However, it is unclear how these error bounds depend on the distributions of the second-stage cost vector q. In this paper, we derive parametric error bounds whose dependence on the distribution of q is explicit: they scale linearly in the expected value of the ?1-norm of q.  相似文献   
4.
Predicting the onset of non-spherical oscillations of bubbles in soft matter is a fundamental cavitation problem with implications to sonoprocessing, polymeric materials synthesis, and biomedical ultrasound applications. The shape stability of a bubble in a Kelvin-Voigt viscoelastic medium with nonlinear elasticity, the simplest constitutive model for soft solids, is analytically investigated and compared to experiments. Using perturbation methods, we develop a model reducing the equations of motion to two sets of evolution equations: a Rayleigh-Plesset-type equation for the mean (volume-equivalent) bubble radius and an equation for the non-spherical mode amplitudes. Parametric instability is predicted by examining the natural frequency and the Mathieu equation for the non-spherical modes, which are obtained from our model. Our theoretical results show good agreement with published experiments of the shape oscillations of a bubble in a gelatin gel. We further examine the impact of viscoelasticity on the time evolution of non-spherical mode amplitudes. In particular, we find that viscosity increases the damping rate, thus suppressing the shape instability, while shear modulus increases the natural frequency, which changes the unstable mode. We also explain the contributions of rotational and irrotational fields to the viscoelastic stresses in the surroundings and at the bubble surface, as these contributions affect the damping rate and the unstable mode. Our analysis on the role of viscoelasticity is potentially useful to measure viscoelastic properties of soft materials by experimentally observing the shape oscillations of a bubble.  相似文献   
5.
In this article, the cascaded second-order nonlinear phase shifts induced in the signal wave are studied using the three-wave parametric interaction in a four-layered QPM leaky waveguide configuration in Z-cut LiNbO 3 . In this interaction, the pump-andsignal waves are guided modes and the idler is radiated into the substrate. We have analyzed the nonlinear phase shifts induced in the signal wave due to cascaded second-order effects, as a function of different waveguide parameters. These studies should find application in realizing practical all-optical signal processing devices.  相似文献   
6.
In this article, using the nonlinear scalarization approach by virtue of the nonlinear scalarization function, commonly known as the Gerstewitz function in the theory of vector optimization, Hölder continuity of solution mappings for both set-valued and single-valued cases to parametric vector equilibrium problems is studied. The nonlinear scalarization function is a powerful tool that plays a key role in the proofs, and its main properties (such as sublinearity, continuity, convexity) are fully employed. Especially, its locally and globally Lipschitz properties are provided and the Lipschitz property is first exploited to investigate the Hölder continuity of solutions.  相似文献   
7.
We propose a new method for measuring electron beam profiles using parametric X-ray radiation. In this method, a pinhole is placed between the source of parametric X-ray radiation and a two-dimensional X-ray detector, and the beam profile can be reconstructed on the detector, i.e., based on the principle of a pinhole camera. The profiles are in good agreement with the results obtained using a standard method with optical transition radiation. This method may prove useful to measure profiles of electron beams with short bunch lengths in recent advanced linear accelerators.  相似文献   
8.
Incomplete data models typically involve strong untestable assumptions about the missing data distribution. As inference may critically depend on them, the importance of sensitivity analysis is well recognized. Molenberghs, Kenward, and Goetghebeur proposed a formal frequentist approach to sensitivity analysis which distinguishes ignorance due to unintended incompleteness from imprecision due to finite sampling by design. They combine both sources of variation into uncertainty. This article develops estimation tools for ignorance and uncertainty concerning regression coefficients in a complete data model when some of the intended outcome values are missing. Exhaustive enumeration of all possible imputations for the missing data requires enormous computational resources. In contrast, when the boundary of the occupied region is of greatest interest, reasonable computational efficiency may be achieved via the imputation towards directional extremes (IDE) algorithm. This is a special imputation method designed to mark the boundary of the region by maximizing the direction of change of the complete data estimator caused by perturbations to the imputed outcomes. For multi-dimensional parameters, a dimension reduction approach is considered. Additional insights are obtained by considering structures within the region, and by introducing external knowledge to narrow the boundary to useful proportions. Special properties hold for the generalized linear model. Examples from a Kenyan HIV study will illustrate the points.  相似文献   
9.
We analyze the concept of credibility in claim frequency in two generalized count models–Mittag-Leffler and Weibull count models–which can handle both underdispersion and overdispersion in count data and nest the commonly used Poisson model as a special case. We find evidence, using data from a Danish insurance company, that the simple Poisson model can set the credibility weight to one even when there are only three years of individual experience data resulting from large heterogeneity among policyholders, and in doing so, it can thus break down the credibility model. The generalized count models, on the other hand, allow the weight to adjust according to the number of years of experience available. We propose parametric estimators for the structural parameters in the credibility formula using the mean and variance of the assumed distributions and a maximum likelihood estimation over a collective data. As an example, we show that the proposed parameters from Mittag-Leffler provide weights that are consistent with the idea of credibility. A simulation study is carried out investigating the stability of the maximum likelihood estimates from the Weibull count model. Finally, we extend the analyses to multidimensional lines and explain how our approach can be used in selecting profitable customers in cross-selling; customers can now be selected by estimating a function of their unknown risk profiles, which is the mean of the assumed distribution on their number of claims.  相似文献   
10.
以自启动被动锁模掺镱光纤堆积脉冲激光器为种子源,采用非共线相位匹配的方法,进行了光参量啁啾脉冲放大器的实验研究,得到了两级放大总增益为1.1×107,单脉冲能量为11 mJ,能量稳定性小于2% rms,8 nm的放大谱宽.实验结果表明,采用这种结构的光参量啁啾脉冲放大器,放大增益高,系统稳定、结构紧凑、便于调节,同时通过调节种子源中的堆积器,可以得到不同宽度的放大信号脉冲.  相似文献   
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