In this paper, we propose the novel p-branch-and-bound method for solving two-stage stochastic programming problems whose deterministic equivalents are represented by non-convex mixed-integer quadratically constrained quadratic programming (MIQCQP) models. The precision of the solution generated by the p-branch-and-bound method can be arbitrarily adjusted by altering the value of the precision factor p. The proposed method combines two key techniques. The first one, named p-Lagrangian decomposition, generates a mixed-integer relaxation of a dual problem with a separable structure for a primal non-convex MIQCQP problem. The second one is a version of the classical dual decomposition approach that is applied to solve the Lagrangian dual problem and ensures that integrality and non-anticipativity conditions are met in the optimal solution. The p-branch-and-bound method's efficiency has been tested on randomly generated instances and demonstrated superior performance over commercial solver Gurobi. This paper also presents a comparative analysis of the p-branch-and-bound method efficiency considering two alternative solution methods for the dual problems as a subroutine. These are the proximal bundle method and Frank-Wolfe progressive hedging. The latter algorithm relies on the interpolation of linearisation steps similar to those taken in the Frank-Wolfe method as an inner loop in the classic progressive hedging.
相關內容
In this work, we couple a high-accuracy phase-field fracture reconstruction approach iteratively to fluid-structure interaction. The key motivation is to utilize phase-field modelling to compute the fracture path. A mesh reconstruction allows a switch from interface-capturing to interface-tracking in which the coupling conditions can be realized in a highly accurate fashion. Consequently, inside the fracture, a Stokes flow can be modelled that is coupled to the surrounding elastic medium. A fully coupled approach is obtained by iterating between the phase-field and the fluid-structure interaction model. The resulting algorithm is demonstrated for several numerical examples of quasi-static brittle fractures. We consider both stationary and quasi-stationary problems. In the latter, the dynamics arise through an incrementally increasing given pressure.
Permutation tests are widely recognized as robust alternatives to tests based on normal theory. Random permutation tests have been frequently employed to assess the significance of variables in linear models. Despite their widespread use, existing random permutation tests lack finite-sample and assumption-free guarantees for controlling type I error in partial correlation tests. To address this ongoing challenge, we have developed a conformal test through permutation-augmented regressions, which we refer to as PALMRT. PALMRT not only achieves power competitive with conventional methods but also provides reliable control of type I errors at no more than $2\alpha$, given any targeted level $\alpha$, for arbitrary fixed designs and error distributions. We have confirmed this through extensive simulations. Compared to the cyclic permutation test (CPT) and residual permutation test (RPT), which also offer theoretical guarantees, PALMRT does not compromise as much on power or set stringent requirements on the sample size, making it suitable for diverse biomedical applications. We further illustrate the differences in a long-Covid study where PALMRT validated key findings previously identified using the t-test after multiple corrections, while both CPT and RPT suffered from a drastic loss of power and failed to identify any discoveries. We endorse PALMRT as a robust and practical hypothesis test in scientific research for its superior error control, power preservation, and simplicity. An R package for PALMRT is available at \url{//github.com/LeyingGuan/PairedRegression}.
This paper proposes a method for analyzing a series of potential motions in a coupling-tiltable aerial-aquatic quadrotor based on its nonlinear dynamics. Some characteristics and constraints derived by this method are specified as Singular Thrust Tilt Angles (STTAs), utilizing to generate motions including planar motions. A switch-based control scheme addresses issues of control direction uncertainty inherent to the mechanical structure by incorporating a saturated Nussbaum function. A high-fidelity simulation environment incorporating a comprehensive hydrodynamic model is built based on a Hardware-In-The-Loop (HITL) setup with Gazebo and a flight control board. The experiments validate the effectiveness of the absolute and quasi planar motions, which cannot be achieved by conventional quadrotors, and demonstrate stable performance when the pitch or roll angle is activated in the auxiliary control channel.
In this work we propose an adaptive multilevel version of subset simulation to estimate the probability of rare events for complex physical systems. Given a sequence of nested failure domains of increasing size, the rare event probability is expressed as a product of conditional probabilities. The proposed new estimator uses different model resolutions and varying numbers of samples across the hierarchy of nested failure sets. In order to dramatically reduce the computational cost, we construct the intermediate failure sets such that only a small number of expensive high-resolution model evaluations are needed, whilst the majority of samples can be taken from inexpensive low-resolution simulations. A key idea in our new estimator is the use of a posteriori error estimators combined with a selective mesh refinement strategy to guarantee the critical subset property that may be violated when changing model resolution from one failure set to the next. The efficiency gains and the statistical properties of the estimator are investigated both theoretically via shaking transformations, as well as numerically. On a model problem from subsurface flow, the new multilevel estimator achieves gains of more than a factor 60 over standard subset simulation for a practically relevant relative error of 25%.
Uplift modeling, also known as individual treatment effect (ITE) estimation, is an important approach for data-driven decision making that aims to identify the causal impact of an intervention on individuals. This paper introduces a new benchmark dataset for uplift modeling focused on churn prediction, coming from a telecom company in Belgium, Orange Belgium. Churn, in this context, refers to customers terminating their subscription to the telecom service. This is the first publicly available dataset offering the possibility to evaluate the efficiency of uplift modeling on the churn prediction problem. Moreover, its unique characteristics make it more challenging than the few other public uplift datasets.
Singularly perturbed boundary value problems pose a significant challenge for their numerical approximations because of the presence of sharp boundary layers. These sharp boundary layers are responsible for the stiffness of solutions, which leads to large computational errors, if not properly handled. It is well-known that the classical numerical methods as well as the Physics-Informed Neural Networks (PINNs) require some special treatments near the boundary, e.g., using extensive mesh refinements or finer collocation points, in order to obtain an accurate approximate solution especially inside of the stiff boundary layer. In this article, we modify the PINNs and construct our new semi-analytic SL-PINNs suitable for singularly perturbed boundary value problems. Performing the boundary layer analysis, we first find the corrector functions describing the singular behavior of the stiff solutions inside boundary layers. Then we obtain the SL-PINN approximations of the singularly perturbed problems by embedding the explicit correctors in the structure of PINNs or by training the correctors together with the PINN approximations. Our numerical experiments confirm that our new SL-PINN methods produce stable and accurate approximations for stiff solutions.
In this study, we present a precise anisotropic interpolation error estimate for the Morley finite element method (FEM) and apply it to fourth-order elliptical equations. We did not impose a shape-regularity mesh condition for the analysis. Therefore, anisotropic meshes can be used. The main contributions of this study include providing new proof of the consistency term. This enabled us to obtain an anisotropic consistency error estimate. The core idea of the proof involves using the relationship between the Raviart--Thomas and Morley finite element spaces. Our results show optimal convergence rates and imply that the modified Morley FEM may be effective for errors.
In this article, we propose and study a stochastic preconditioned Douglas-Rachford splitting method to solve saddle-point problems which have separable dual variables. We prove the almost sure convergence of the iteration sequences in Hilbert spaces for a class of convexconcave and nonsmooth saddle-point problems. We also provide the sublinear convergence rate for the ergodic sequence with respect to the expectation of the restricted primal-dual gap functions. Numerical experiments show the high efficiency of the proposed stochastic preconditioned Douglas-Rachford splitting methods.
In this paper, we study power series with coefficients equal to a product of a generic sequence and an explicitly given function of a positive parameter expressible in terms of the Pochhammer symbols. Four types of such series are treated. We show that logarithmic concavity (convexity) of the generic sequence leads to logarithmic concavity (convexity) of the sum of the series with respect to the argument of the explicitly given function. The logarithmic concavity (convexity) is derived from a stronger property, namely, positivity (negativity) of the power series coefficients of the so-called generalized Tur\'{a}nian. Applications to special functions such as the generalized hypergeometric function and the Fox-Wright function are also discussed.
We propose a new method for estimating causal effects in longitudinal/panel data settings that we call generalized difference-in-differences. Our approach unifies two alternative approaches in these settings: ignorability estimators (e.g., synthetic controls) and difference-in-differences (DiD) estimators. We propose a new identifying assumption -- a stable bias assumption -- which generalizes the conditional parallel trends assumption in DiD, leading to the proposed generalized DiD framework. This change gives generalized DiD estimators the flexibility of ignorability estimators while maintaining the robustness to unobserved confounding of DiD. We also show how ignorability and DiD estimators are special cases of generalized DiD. We then propose influence-function based estimators of the observed data functional, allowing the use of double/debiased machine learning for estimation. We also show how generalized DiD easily extends to include clustered treatment assignment and staggered adoption settings, and we discuss how the framework can facilitate estimation of other treatment effects beyond the average treatment effect on the treated. Finally, we provide simulations which show that generalized DiD outperforms ignorability and DiD estimators when their identifying assumptions are not met, while being competitive with these special cases when their identifying assumptions are met.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191