Learning Convex Optimization Models

A convex optimization model predicts an output from an input by solving a convex optimization problem.The class of convex optimization models is large,and includes as special cases many well-known models like linear and logistic regression.We propose a heuristic for learning the parameters in a convex optimization model given a dataset of input-output pairs,using recently developed methods for differentiating the solution of a convex optimization problem with respect to its parameters.We describe three general classes of convex optimization models,maximum a posteriori(MAP)models,utility maximization models,and agent models,and present a numerical experiment for each.

AERODYNAMIC OPTIMIZATION DESIGN OF LOW ASPECT RATIO TRANSONIC TURBINE STAGE

The advanced optimization method named as adaptive range differential evolution （ARDE） is developed. The optimization performance of ARDE is demonstrated using a typical mathematical test and compared with the standard genetic algorithm and differential evolution. Combined with parallel ARDE, surface modeling method and Navier-Stokes solution, a new automatic aerodynamic optimization method is presented. A low aspect ratio transonic turbine stage is optimized for the maximization of the isentropic efficiency with forty-one design variables in total. The coarse-grained parallel strategy is applied to accelerate the design process using 15 CPUs. The isentropic efficiency of the optimum design is 1.6% higher than that of the reference design. The aerodynamic performance of the optimal design is much better than that of the reference design.

HARDY-LITTLEWOOD-POLYA INEQUALITY FOR A LINEAR DIFFERENTIAL OPERATOR AND SOME RELATED OPTIMAL PROBLEMS

In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.

Strip width spread prediction in rough rolling process based on mechanism modeling and optimization

Aiming at the problems of low accuracy and poor robustness that existed in the current hot rolling strip width spread model,an improved strip spread prediction model based on a material forming mechanism and Bayesian optimized adaptive differential evolution algorithm(BADE)was proposed.At first,we improved the original spread mechanism model by adding the weight and bias term to enhance the model robustness based on rolling temperature.Then,the BADE algorithm was proposed to optimize the improved spread mechanism model.The optimization algorithm is based on a novel adaptive differential evolution algorithm,which can effectively achieve the global optimal solution.Finally,the prediction performances of five machine learning algorithms were compared in experiments.The results show that the prediction accuracy of the improved spread model is obviously better than that of the machine learning algorithms,which proves the effectiveness of the proposed method.

Application of smoothing technique on twin support vector hypersphere

In order to improve the learning speed and reduce computational complexity of twin support vector hypersphere(TSVH),this paper presents a smoothed twin support vector hypersphere(STSVH)based on the smoothing technique.STSVH can generate two hyperspheres with each one covering as many samples as possible from the same class respectively.Additionally,STSVH only solves a pair of unconstraint differentiable quadratic programming problems(QPPs)rather than a pair of constraint dual QPPs which makes STSVH faster than the TSVH.By considering the differentiable characteristics of STSVH,a fast Newton-Armijo algorithm is used for solving STSVH.Numerical experiment results on normally distributed clustered datasets(NDC)as well as University of California Irvine(UCI)data sets indicate that the significant advantages of the proposed STSVH in terms of efficiency and generalization performance.

Hybrid Meta-Model Based Design Space Differentiation Method for Expensive Problems

In this work,a hybrid meta-model based design space differentiation（HMDSD）method is proposed for practical problems.In the proposed method,an iteratively reduced promising region is constructed using the expensive points,with two different search strategies respectively applied inside and outside the promising region.Besides,the hybrid meta-model strategy applied in the search process makes it possible to solve the complex practical problems.Tested upon a serial of benchmark math functions,the HMDSD method shows great efficiency and search accuracy.On top of that,a practical lightweight design demonstrates its superior performance.