PARALLEL MINIMIZATION ALGORITHMS by GENERALIZED SUBDIFFERENTIABILITY

Abstract Recently a, monotone generalized directional derixrative has been introduced for Lipschitz functions. This concept has been applied to represent and optimize nonsmooth functions. The second a.pplication result,ed relevant for parallel computing, by allowing to define minimization algorithms with high degree of inherent parallelism. The paper presents first the theoretical background, namely the notions of monotone generalized directional derivative and monotone generalized subdifferential. Then it defines the tools for the procedures, that is a necessary optimality condition and a steel>est descent direction. Therefore the minimization algorithms are outlined. Successively the used architectures and the performed numerical expertence are described, by listing and commenting the t.ested functions and the obtained results.

AN ALGORITHM OF UNCONSTRAINED MINIMIZATION WITHOUT DERIVATIVE AND ITS CONVERGENCE

In [1] the unconstrained minimization problem was considered and presented an algorithm without derivative. But the terminative conditions and convergence proof of the algorithm were not given. In this paper, we present a revised algorithm and prove its convergence.

Application of k-person and k-task maximal efficiency assignment algorithm to water piping repair

Solving the absent assignment problem of the shortest time limit in a weighted bipartite graph with the minimal weighted k-matching algorithm is unsuitable for situations in which large numbers of problems need to be addressed by large numbers of parties. This paper simplifies the algorithm of searching for the even alternating path that contains a maximal element using the minimal weighted k-matching theorem and intercept graph. A program for solving the maximal efficiency assignment problem was compiled. As a case study, the program was used to solve the assignment problem of water piping repair in the case of a large number of companies and broken pipes, and the validity of the program was verified.

Study and application of an improved four-dimensional variational assimilation system based on the physical-space statistical analysis for the South China Sea

The four-dimensional variational assimilation(4D-Var)has been widely used in meteorological and oceanographic data assimilation.This method is usually implemented in the model space,known as primal approach(P4D-Var).Alternatively,physical space analysis system(4D-PSAS)is proposed to reduce the computation cost,in which the 4D-Var problem is solved in physical space(i.e.,observation space).In this study,the conjugate gradient(CG)algorithm,implemented in the 4D-PSAS system is evaluated and it is found that the non-monotonic change of the gradient norm of 4D-PSAS cost function causes artificial oscillations of cost function in the iteration process.The reason of non-monotonic variation of gradient norm in 4D-PSAS is then analyzed.In order to overcome the non-monotonic variation of gradient norm,a new algorithm,Minimum Residual(MINRES)algorithm,is implemented in the process of assimilation iteration in this study.Our experimental results show that the improved 4D-PSAS with the MINRES algorithm guarantees the monotonic reduction of gradient norm of cost function,greatly improves the convergence properties of 4D-PSAS as well,and significantly restrains the numerical noises associated with the traditional 4D-PSAS system.

ITERATIVE l1 MINIMIZATION FOR NON-CONVEX COMPRESSED SENSING

An algorithmic framework, based on the difference of convex functions algorithm （D- CA）, is proposed for minimizing a class of concave sparse metrics for compressed sensing problems. The resulting algorithm iterates a sequence ofl1 minimization problems. An exact sparse recovery theory is established to show that the proposed framework always improves on the basis pursuit （l1 minimization） and inherits robustness from it. Numerical examples on success rates of sparse solution recovery illustrate further that, unlike most existing non-convex compressed sensing solvers in the literature, our method always out- performs basis pursuit, no matter how ill-conditioned the measurement matrix is. Moreover, the iterative l1 （ILl） algorithm lead by a wide margin the state-of-the-art algorithms on l1/2 and logarithimic minimizations in the strongly coherent （highly ill-conditioned） regime, despite the same objective functions. Last but not least, in the application of magnetic resonance imaging （MRI）, IL1 algorithm easily recovers the phantom image with just 7 line projections.

Social Choice Meets Graph Drawing: How to Get Subexponential Time Algorithms for Ranking and Drawing Problems

We analyze a common feature of p-Kemeny AGGregation（p-KAGG） and p-One-Sided Crossing Minimization（p-OSCM） to provide new insights and findings of interest to both the graph drawing community and the social choice community. We obtain parameterized subexponential-time algorithms for p-KAGG—a problem in social choice theory—and for p-OSCM—a problem in graph drawing. These algorithms run in time O＊（2O（√k log k））,where k is the parameter, and significantly improve the previous best algorithms with running times O.1.403k/and O.1.4656k/, respectively. We also study natural ＂above-guarantee＂ versions of these problems and show them to be fixed parameter tractable. In fact, we show that the above-guarantee versions of these problems are equivalent to a weighted variant of p-directed feedback arc set. Our results for the above-guarantee version of p-KAGG reveal an interesting contrast. We show that when the number of ＂votes＂ in the input to p-KAGG is odd the above guarantee version can still be solved in time O＊（2O（√k log k））, while if it is even then the problem cannot have a subexponential time algorithm unless the exponential time hypothesis fails（equivalently, unless FPT D M[1]）.

General noise support vector regression with non-constant uncertainty intervals for solar radiation prediction

General noise cost functions have been recently proposed for support vector regression(SVR). When applied to tasks whose underlying noise distribution is similar to the one assumed for the cost function, these models should perform better than classical -SVR. On the other hand, uncertainty estimates for SVR have received a somewhat limited attention in the literature until now and still have unaddressed problems. Keeping this in mind,three main goals are addressed here. First, we propose a framework that uses a combination of general noise SVR models with naive online R minimization algorithm(NORMA) as optimization method, and then gives nonconstant error intervals dependent upon input data aided by the use of clustering techniques. We give theoretical details required to implement this framework for Laplace, Gaussian, Beta, Weibull and Marshall–Olkin generalized exponential distributions. Second, we test the proposed framework in two real-world regression problems using data of two public competitions about solar energy. Results show the validity of our models and an improvement over classical -SVR. Finally, in accordance with the principle of reproducible research, we make sure that data and model implementations used for the experiments are easily and publicly accessible.

Mathematical Programming Solution for the Frictional Contact Multipole BEM

This paper presents a new mathematical model for the highly nonlinear problem of frictional con- tact. A programming model, multipole boundary element method (BEM), was developed for 3-D elastic con- tact with friction to replace the Monte Carlo method. A numerical example shows that the optimization pro- gramming model for the point-to-surface contact with friction and the fast optimization generalized minimal residual algorithm (GMRES(m)) significantly improve the analysis of such problems relative to the conven- tional BEM.