On Second-order Sufficient Conditions in Constrained Nonsmooth Optimization

In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednarik and K. Pastor, Math. Program. Ser. A, 113（2008）, 283-298] to constrained optimization problems.

A NEW DERIVATIVE FREE OPTIMIZATION METHOD BASED ON CONIC INTERPOLATION MODEL

In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.

A TRUST REGION METHOD WITH A CONIC MODEL FOR NONLINEARLY CONSTRAINED OPTIMIZATION

Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The advantages of the above two methods can be combined to form a more powerful method for constrained optimization. The trust region subproblem of our method is to minimize a conic function subject to the linearized constraints and trust region bound. At the same time, the new algorithm still possesses robust global properties. The global convergence of the new algorithm under standard conditions is established.

Optimal Multiperiodic Control for Inventory Coupled Systems: A Multifrequency Second-Order Test

A complex autonomous inventory coupled system is considered. It can take, for example, the form of a network of chemical or biochemical reactors, where the inventory interactions perform the recycling of by-products between the subsystems. Because of the flexible subsystems interactions, each of them can be operated with their own periods utilizing advantageously their dynamic properties. A multifrequency second-order test generalizing the p-test for single systems is described. It can be used to decide which kind of the operation (the static one, the periodic one or the multiperiodic one) will intensify the productivity of a complex system. An illustrative example of the multiperiodic optimization of a complex chemical production system is presented.

Multiconstraint adaptive three-dimensional guidance law using convex optimization

The traditional guidance law only guarantees the accuracy of attacking a target. However, the look angle and acceleration constraints are indispensable in applications. A new adaptive three-dimensional proportional navigation(PN) guidance law is proposed based on convex optimization. Decomposition of the three-dimensional space is carried out to establish threedimensional kinematic engagements. The constraints and the performance index are disposed by using the convex optimization method. PN guidance gains can be obtained by solving the optimization problem. This solution is more rapid and programmatic than the traditional method and provides a foundation for future online guidance methods, which is of great value for engineering applications.

Advanced algorithms for retrieving pileup peaks of digital alpha spectroscopy using antlions and particle swarm optimizations

Optimization algorithms are applied to resolve the second-order pileup(SOP)issue from high counting rates occurring in digital alpha spectroscopy.These are antlion optimizer(ALO)and particle swarm optimization(PSO)algorithms.Both optimization algorithms are coupled to one of the three proposed peak finder algorithms.Three custom time-domain algorithms are proposed for retrieving SOP peaks,namely peak seek,slope tangent,and fast array algorithms.In addition,an average combinational algorithm is applied.The time occurrence of the retrieved peaks is tested for an elimination of illusive pulses.Conventional methods are inaccurate and timeconsuming.ALO and PSO optimizations are used for the localization of retrieved peaks.Optimum cost values that achieve the best fitness values are demonstrated.Thus,the optimum positions of the detected peak heights are achieved.Evaluation metrics of the optimized algorithms and their influences on the retrieved peaks parameters are established.Comparisons among such algorithms are investigated,and the algorithms are inspected in terms of their computational time and average error.The peak seek algorithm achieves the lowest average computational error for pulse parameters(amplitude and position).However,the fast array algorithm introduces the largest average error for pulse parameters.In addition,the peak seek algorithm coupled with an ALO or PSO algorithm is observed to realize a better performance in terms of the optimum cost and computational time.By contrast,the performance of the peak seek recovery algorithm is improved using the PSO.Furthermore,the computational time of the peak optimization using the PSO is much better than that of the ALO algorithm.As a final conclusion,the accuracy of the peaks detected by the PSO surpasses that for the peaks detected by the ALO.The implemented peak retrieval algorithms are validated through a comparison with experimental results from previous studies.The proposed algorithms achieve a notable precision for compensation of the SOP peaks within the alpha ray spectroscopy at a high counting rate.

Robust Source Localization in Shallow Water Based on Vector Optimization

Owing to the multipath effect, the source localization in shallow water has been an area of active interest. However, most methods for source localization in shallow water are sensitive to the assumed model of the underwater environment and have poor robustness against the underwater channel uncertainty, which limit their further application in practical engineering. In this paper, a new method of source localization in shallow water, based on vector optimization concept, is described, which is highly robust against environmental factors affecting the localization, such as the channel depth, the bottom reflection coefficients, and so on. Through constructing the uncertainty set of the source vector errors and extracting the multi-path sound rays from the sea surface and bottom, the proposed method can accurately localize one or more sources in shallow water dominated by multipath propagation. It turns out that the natural formulation of our approach involves minimization of two quadratic functions subject to infinitely many nonconvex quadratic constraints. It shows that this problem （originally intractable） can be reformulated in a convex form as the so-called second-order cone program （SOCP） and solved efficiently by using the well-established interior point method, such as the sottware tool, SeDuMi. Computer simulations show better performance of the proposed method as compared with existing algorithms and establish a theoretical foundation for the practical engineering application.

A VU-decomposition method for a second-order cone programming problem

A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential corresponding to the penalty function and some results of itsvu-decomposition are given. Under a certain condition, a twice continuously differentiable trajectory is computed to produce a second-order expansion of the objective function. A conceptual algorithm for solving this problem with a superlinear convergence rate is given.

Solution of Second-Order Ordinary Differential Equations via Simulated Annealing

In this paper, we approach the problem of obtaining approximate solution of second-order initial value problems by converting it to an optimization problem. It is assumed that the solution can be approximated by a polynomial. The coefficients of the polynomial are then optimized using simulated annealing technique. Numerical examples with good results show the accuracy of the proposed approach compared with some existing methods.

Experimental Study and 3D CFD Analysis on the Optimization of Throttle Angle for a Convergent Vortex Tube

会聚类型的旋涡试管(vt ) 与的七调整不同扼杀角度被使用。调整被做在 vt 内在冷、热的温度落下以及流动结构上分析如此的角度的影响。试验性的安装被设计，并且测试在从 0.45 ～ 0.65 MPa 的注射压力在不同会聚的 vt 配置上被执行。throttle 阀门的角度在 30 湯愠 ? 桴 ? 潮据癯污湥 ? 湩整慲瑣潩 ? 潤潮之间被安排吗？？

Wheel Profile Optimization of Speed-up Freight Train Based on Multi-population Genetic Algorithm

The geometric shape of the wheel tread is mathematically expressed,and geometric parameters affecting the shape of the wheel were extracted as design variables.The vehicle dynamics simulation model was established based on the vehicle suspension parameters and track conditions of the actual operation,and the comprehensive dynamic parameters of the vehicle were taken as the design objectives.The matching performance of the wheel equivalent conicity with the vehicle and track parameters was discussed,and the best equivalent conicity was determined as the constraint condition of the optimization problem;a numerical calculation program is written to solve the optimization model based on a multi-population genetic algorithm.The results show that the algorithm has a fast calculation speed and good convergence.Compared with the LM profile,the two optimized profiles effectively reduce the wheelset acceleration and improve the lateral stability of the bogie and vehicle stability during straight running.Due to the optimized profile increases the equivalent conicity under larger lateral displacement of the wheelset,the lateral wheel-rail force,derailment coefficient,wheel load reduction rate,and wear index are reduced when the train passes through the curve line.This paper provides a feasible way to ensure the speed-up operation of a freight train.

速度160 km/h动力集中动车组动力车车轮踏面优化研究

文中针对某型160 km/h动力集中动车组动力车在车轮旋修后横向平稳性显著变差问题进行了原因分析,指出了TB/T 449标准中JM3薄轮缘外形轮廓与JM3型外形轮廓的差异,从而导致轮轨匹配等效锥度较低为该晃车的主要原因。文中提出了轮缘厚度分别为32、30 mm的旋修用优化薄轮缘踏面外形并对踏面有效性、安全性进行了计算分析和试验验证。

Pointwise Second-Order Necessary Conditions for Stochastic Optimal Control with Jump Diffusions

In this paper,we establish a second-order necessary conditions for stochastic optimal control for jump diffusions.The controlled system is described by a stochastic differential systems driven by Poisson random measure and an independent Brownian motion.The control domain is assumed to be convex.Pointwise second-order maximum principle for controlled jump diffusion in terms of the martingale with respect to the time variable is proved.The proof of the main result is based on variational approach using the stochastic calculus of jump diffusions and some estimates on the state processes.

Day-ahead Optimization Schedule for Gas-electric Integrated Energy System Based on Second-order Cone Programming

This paper proposes an optimal day-ahead opti-mization schedule for gas-electric integrated energy system(IES)considering the bi-directional energy flow.The hourly topology of electric power system(EPS),natural gas system(NGS),energy hubs(EH)integrated power to gas(P2G)unit,are modeled to minimize the day-ahead operation cost of IES.Then,a second-order cone programming(SOCP)method is utilized to solve the optimization problem,which is actually a mixed integer nonconvex and nonlinear programming issue.Besides,cutting planes are added to ensure the exactness of the global optimal solution.Finally,simulation results demonstrate that the proposed optimization schedule can provide a safe,effective and economical day-ahead scheduling scheme for gas-electric IES.

Primal-dual Interior-point Algorithms for Second-order Cone Optimization Based on a New Parametric Kernel Function

A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and quadratic. Some new tools for the analysis of the algorithms are proposed. The complexity bounds of O（√Nlog N log N/ε） for large-update methods and O（√Nlog N/ε） for smallupdate methods match the best known complexity bounds obtained for these methods. Numerical tests demonstrate the behavior of the algorithms for different results of the parameters p and q.

Distributed Second-Order Continuous-Time Optimization via Adaptive Algorithm with Nonuniform Gradient Gains

This paper addresses the distributed adaptive optimization problem over second-order multi-agent networks(MANs)with nonuniform gradient gains.A general convex function consisting of a sum of local differentiable convex functions is chosen as the team objective function.First,based on the local information of each agent’s neighborhood,a novel distributed adaptive optimization algorithm with nonuniform gradient gains is designed,where these gains only have relations with agents’own states.And then,the original closed-loop system is changed into an equivalent one by taking a coordination transformation.Moreover,it is proved that the states including positions and velocities of all agents are bounded by constructing a Lyapunov function provided that the initial values are given.By the theory of Lyapunov stability,it is shown that all agents can finally reach an agreement and their position states converge to the optimal solution of the team objective function asymptotically.Finally,the effectiveness of the obtained theoretical results is demonstrated by several simulation examples.

Second-Order Optimality Conditions for Multiobjective Optimization Whose Order Induced by Second-Order Cone

This paper is devoted to developing first-order necessary,second-order necessary,and second-order sufficient optimality conditions for a multiobjective optimization problem whose order is induced by a finite product of second-order cones(here named as Q-multiobjective optimization problem).For an abstract-constrained Q-multiobjective optimization problem,we derive two basic necessary optimality theorems for weak efficient solutions and a second-order sufficient optimality theorem for efficient solutions.For Q-multiobjective optimization problem with explicit constraints,we demonstrate first-order and second-order necessary optimality conditions under Robinson constraint qualification as well as second-order sufficient optimality conditions under upper second-order regularity for the explicit constraints.As applications,we obtain optimality conditions for polyhedral conic,second-order conic,and semi-definite conic Q-multiobjective optimization problems.

New Second-order Contingent Epiderivatives and Set-valued Optimization Problems

In this paper, we introduce the concept of second-order compound contingent epiderivative for set-valued maps and discuss its relationship to the second-order contingent epiderivative. Simultaneously, we also investigate some special properties of the second-order compound contingent epiderivative. By virtue of the second-order compound contingent epiderivative, we establish some unified second-order sufficient and necessary optimality conditions for set-valued optimization problems. All results in this paper generalize the corresponding results in the literature.

A CLASS OF COLLINEAR SCALING ALGORITHMS FOR UNCONSTRAINED OPTIMIZATON

A Class of Collinear Scaling Algorithms for Unconstrained Optimization. An appealing approach to the solution of nonlinear optimization problems based on conic models of the objective function has been in troduced by Davidon (1980). It leads to a broad class of algorithms which can be considered to generalize the existing quasi-Newton methods. One particular member of this class has been deeply discussed by Sorensen (1980), who has proved some interesting theoretical properties. In this paper, we generalize Sorensen’s technique to Spedicato three-parameter family of variable-metric updates. Furthermore, we point out that the collinear scaling three- parameter family is essentially equivalent to the Spedicato three-parameter family. In addition, numerical expriments have been carried out to compare some colliner scaling algorithms with a straightforward implementation of the BFGS quasi-Newton method.

Quadratic Optimization over a Second-Order Cone with Linear Equality Constraints

This paper studies the nonhomogeneous quadratic programming problem over a second-order cone with linear equality constraints.When the feasible region is bounded,we show that an optimal solution of the problem can be found in polynomial time.When the feasible region is unbounded,a semidefinite programming(SDP)reformulation is constructed to find the optimal objective value of the original problem in polynomial time.In addition,we provide two sufficient conditions,under which,if the optimal objective value is finite,we show the optimal solution of SDP reformulation can be decomposed into the original space to generate an optimal solution of the original problem in polynomial time.Otherwise,a recession direction can be identified in polynomial time.Numerical examples are included to illustrate the effectiveness of the proposed approach.