A PENALTY FUNCTION METHOD FOR THE PRINCIPAL-AGENT PROBLEM WITH AN INFINITE NUMBER OF INCENTIVE-COMPATIBILITY CONSTRAINTS UNDER MORAL HAZARD

In this paper,we propose an iterative algorithm to find the optimal incentive mechanism for the principal-agent problem under moral hazard where the number of agent action profiles is infinite,and where there are an infinite number of results that can be observed by the principal.This principal-agent problem has an infinite number of incentive-compatibility constraints,and we transform it into an optimization problem with an infinite number of constraints called a semi-infinite programming problem.We then propose an exterior penalty function method to find the optimal solution to this semi-infinite programming and illustrate the convergence of this algorithm.By analyzing the optimal solution obtained by the proposed penalty function method,we can obtain the optimal incentive mechanism for the principal-agent problem with an infinite number of incentive-compatibility constraints under moral hazard.

New simple exact penalty function for constrained minimization

By adding one variable to the equality-or inequality-constrained minimization problems, a new simple penalty function is proposed. It is proved to be exact in the sense that under mild assumptions, the local minimizers of this penalty function are precisely the local minimizers of the original problem, when the penalty parameter is sufficiently large.

New exact penalty function for solving constrainedfinite min-max problems

This paper introduces a new exact and smooth penalty function to tackleconstrained min-max problems.By using this new penalty function and adding justone extra variable,a constrained min-max problem is transformed into an unconstrainedoptimization one.It is proved that,under certain reasonable assumptions and when thepenalty parameter is sufficiently large,the minimizer of this unconstrained optimizationproblem is equivalent to the minimizer of the original constrained one.Numerical resultsdemonstrate that this penalty function method is an effective and promising approach forsolving constrained finite min-max problems.

A New Unified Path to Smoothing Nonsmooth Exact Penalty Function for the Constrained Optimization

We propose a new unified path to approximately smoothing the nonsmooth exact penalty function in this paper. Based on the new smooth penalty function, we give a penalty algorithm to solve the constrained optimization problem, and discuss the convergence of the algorithm under mild conditions.

A New Objective Penalty Function Approach for Solving Constrained Minimax Problems

In this paper,a new objective penalty function approach is proposed for solving minimax programming problems with equality and inequality constraints.This new objective penalty function combines the objective penalty and constraint penalty.By the new objective penalty function,a constrained minimax problem is converted to minimizations of a sequence of continuously differentiable functions with a simple box constraint.One can thus apply any efficient gradient minimization methods to solve the minimizations with box constraint at each step of the sequence.Some relationships between the original constrained minimax problem and the corresponding minimization problems with box constraint are established.Based on these results,an algorithm for finding a global solution of the constrained minimax problems is proposed by integrating the particular structure of minimax problems and its global convergence is proved under some conditions.Furthermore,an algorithm is developed for finding a local solution of the constrained minimax problems,with its convergence proved under certain conditions.Preliminary results of numerical experiments with well-known test problems show that satisfactorilyapproximate solutions for some constrained minimax problems can be obtained.

Dynamic Analysis of A Deepwater Drilling Riser with A New Hang-off System

The safety of risers in hang-off states is a vital challenge in offshore oil and gas engineering.A new hang-off system installed on top of risers is proposed for improving the security of risers.This approach leads to a challenging problem:coupling the dynamics of risers with a new hang-off system combined with multiple structures and complex constraints.To accurately analyze the dynamic responses of the coupled system,a coupled dynamic model is established based on the Euler-Bernoulli beam-column theory and penalty function method.A comprehensive analysis method is proposed for coupled dynamic analysis by combining the finite element method and the Newmarkβmethod.An analysis program is also developed in MATLAB for dynamic simulation.The simulation results show that the dynamic performances of the risers at the top part are significantly improved by the new hang-off system,especially the novel design,which includes the centralizer and articulation joint.The bending moment and lateral deformation of the risers at the top part decrease,while the hang-off joint experiences a great bending moment at the bottom of the lateral restraint area which requires particular attention in design and application.The platform navigation speed range under the safety limits of risers expands with the new hang-off system in use.

Trajectory optimization of a reentry vehicle based on artificial emotion memory optimization

The trajectory optimization of an unpowered reentry vehicle via artificial emotion memory optimization(AEMO)is discussed.Firstly,reentry dynamics are established based on multiple constraints and parameterized control variables with finite dimensions are designed.If the constraint is not satisfied,a distance measure and an adaptive penalty function are used to address this scenario.Secondly,AEMO is introduced to solve the trajectory optimization problem.Based on the theories of biology and cognition,the trial solutions based on emotional memory are established.Three search strategies are designed for realizing the random search of trial solutions and for avoiding becoming trapped in a local minimum.The states of the trial solutions are determined according to the rules of memory enhancement and forgetting.As the iterations proceed,the trial solutions with poor quality will gradually be forgotten.Therefore,the number of trial solutions is decreased,and the convergence of the algorithm is accelerated.Finally,a numerical simulation is conducted,and the results demonstrate that the path and terminal constraints are satisfied and the method can realize satisfactory performance.

An improved local radial point interpolation method for transient heat conduction analysis

The smoothing thin plate spline(STPS) interpolation using the penalty function method according to the optimization theory is presented to deal with transient heat conduction problems.The smooth conditions of the shape functions and derivatives can be satisfied so that the distortions hardly occur.Local weak forms are developed using the weighted residual method locally from the partial differential equations of the transient heat conduction.Here the Heaviside step function is used as the test function in each sub-domain to avoid the need for a domain integral.Essential boundary conditions can be implemented like the finite element method(FEM) as the shape functions possess the Kronecker delta property.The traditional two-point difference method is selected for the time discretization scheme.Three selected numerical examples are presented in this paper to demonstrate the availability and accuracy of the present approach comparing with the traditional thin plate spline(TPS) radial basis functions.

Evaluation of a novel Asymmetric Genetic Algorithm to optimize the structural design of 3D regular and irregular steel frames

We propose a new algorithm,named Asymmetric Genetic Algorithm(AGA),for solving optimization problems of steel frames.The AGA consists of a developed penalty function,which helps to find the best generation of the population.The objective function is to minimize the weight of the whole steel structure under the constraint of ultimate loads defined for structural steel buildings by the American Institute of Steel Construction(AISC).Design variables are the cross-sectional areas of elements(beams and columns)that are selected from the sets of side-flange shape steel sections provided by the AISC.The finite element method(FEM)is utilized for analyzing the behavior of steel frames.A 15-storey three-bay steel planar frame is optimized by AGA in this study,which was previously optimized by algorithms such as Particle Swarm Optimization(PSO),Particle Swarm Optimizer with Passive Congregation(PSOPC),Particle Swarm Ant Colony Optimization(HPSACO),Imperialist Competitive Algorithm(ICA),and Charged System Search(CSS).The results of AGA such as total weight of the structure and number of analyses are compared with the results of these algorithms.AGA performs better in comparison to these algorithms with respect to total weight and number of analyses.In addition,five numerical examples are optimized by AGA,Genetic Algorithm(GA),and optimization modules of SAP2000,and the results of them are compared.The results show that AGA can decrease the time of analyses,the number of analyses,and the total weight of the structure.AGA decreases the total weight of regular and irregular steel frame about 11.1%and 26.4%in comparing with the optimized results of SAP2000,respectively.

Prediction of electric-powered fixed-wing UAV endurance

To overcome the problems encountered in predicting the endurance of electricpowered fixed-wing unmanned aerial vehicles(UAVs),which were stemmed from the dynamic changes in electric power system efficiency and battery discharge characteristics under different operating conditions,the required battery power model and battery discharge model were studied.The required battery power model was determined using an approximate model of electric power system efficiency based on wind tunnel testing and the self-adaptive penalty function.Furthermore,current correction and ambient temperature correction terms were proposed for the trained Kriging model representing the discharge characteristics under standard operation,and then the discharged capacity-terminal voltage model was established.Through numerical integration of this model with the required battery power model,the electric-powered fixed-wing UAV endurance prediction model was obtained.Laboratory tests indicated that the proposed endurance model could precisely calculate the battery discharge time and accurately describe the battery discharge process.The similarity of the theoretical and flight test results reflected the accuracy of the proposed endurance model as well as the importance of considering dynamic changes in power system efficiency in endurance calculations.The proposed endurance model meeting precision requirements can be used in practical engineering applications.

Emergency airport site selection using global subdivision grids

The occurrence of large-magnitude disasters has significantly aroused public attention regarding diversified site selection of emergency facilities.In particular,emergency airport site selection(EASS)is highly complicated,and relevant research is rarely conducted.Emergency airport site selection is a scenario with a wide spatiotemporal range,massive data,and complex environmental information,while traditional facility site selection methods may not be applicable to a large-scale time-varying airport environment.In this work,an emergency airport site selection application is presented based on the GeoSOT-3D global subdivision grid model,which has demonstrated good suitability of the discrete global grid system as a spatial data structure for site selection.This paper proposes an objective function that adds a penalty factor to solve the constraints of coverage and the environment in airport construction.Through multiple iterations of the simulated annealing algorithm,the optimal airport construction location can be selected from multiple preselected points.With experimental verifications,this research may effectively and reasonably solve the emergency airport site selection issue under different circumstances.

A Branch and Bound-Based Algorithm for the Weak Linear Bilevel Programming Problems

最真实世界的优化问题是层次的包含非合作的目的。许多能这些问题被提出以(上面的水平) 首先，客观功能在印射的答案集合上正在被最小化第二(底层) 优化问题。经常上面的水平决定制造者是风险反对的。问题的产生的类被称为弱上下两层的编程问题。这篇论文论述把一个惩罚功能方法嵌进一个分支的一个新算法和界限算法处理一个弱线性上下两层的编程问题。一个例子说明建议算法的可行性。

The Asymptotic Properties of Scad Penalized Generalized Linear Models with Adaptive Designs

This paper discusses the asymptotic properties of the SCAD(smoothing clipped absolute deviation)penalized quasi-likelihood estimator for generalized linear models with adaptive designs,which extend the related results for independent observations to dependent observations.Under certain conditions,the authors proved that the SCAD penalized method correctly selects covariates with nonzero coefficients with probability converging to one,and the penalized quasi-likelihood estimators of non-zero coefficients have the same asymptotic distribution they would have if the zero coefficients were known in advance.That is,the SCAD estimator has consistency and oracle properties.At last,the results are illustrated by some simulations.