The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some *** authors propose the derivative-free optimization algorithm SUSD-TR,whic...
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The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some *** authors propose the derivative-free optimization algorithm SUSD-TR,which combines the SUSD direction based on the covariance matrix of interpolation points and the solution of the trust-region subproblem of the interpolation model function at the current iteration *** analyze the optimization dynamics and convergence of the algorithm *** of the trial step and structure step are *** results show their algorithm’s efficiency,and the comparison indicates that SUSD-TR greatly improves the method’s performance based on the method that only goes along the SUSD *** algorithm is competitive with state-of-the-art mathematical derivative-free optimization algorithms.
This paper considers the quality-of-service (QoS)-based joint beamforming and compression design problem in the downlink cooperative cellular network, where multiple relay-like base stations (BSs), connected to the ce...
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In this paper,we present a novel penalty model called ExPen for optimization over the Stiefel *** from existing penalty functions for orthogonality constraints,ExPen adopts a smooth penalty function without using any ...
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In this paper,we present a novel penalty model called ExPen for optimization over the Stiefel *** from existing penalty functions for orthogonality constraints,ExPen adopts a smooth penalty function without using any first-order derivative of the objective *** show that all the first-order stationary points of ExPen with a sufficiently large penalty parameter are either feasible,namely,are the first-order stationary points of the original optimization problem,or far from the Stiefel ***,the original problem and ExPen share the same second-order stationary ***,the exact gradient and Hessian of ExPen are easy to *** a consequence,abundant algorithm resources in unconstrained optimization can be applied straightforwardly to solve ExPen.
Multiform fractures have a direct impact on the mechanical performance of rock *** accurately identify multiform fractures,the distribution patterns of grayscale and the differential features of fractures in their nei...
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Multiform fractures have a direct impact on the mechanical performance of rock *** accurately identify multiform fractures,the distribution patterns of grayscale and the differential features of fractures in their neighborhoods are *** on this,a multiscale processing algorithm is *** multiscale process is as *** the neighborhood of pixels,a grayscale continuous function is constructed using bilinear interpolation,the smoothing of the grayscale function is realized by Gaussian local filtering,and the grayscale gradient and Hessian matrix are calculated with high *** small-scale blocks,the pixels are classified by adaptively setting the grayscale threshold to identify potential line segments and *** the global image,potential line segments and mini-fillings are spliced together by progressing the block frontier layer-by-layer to identify and mark multiform *** accuracy of identifying multiform fractures is improved by constructing a grayscale continuous function and adaptively setting the grayscale thresholds on small-scale *** the layer-by-layer splicing algorithm is performed only on the domain of the 2-layer small-scale blocks,reducing the *** using rock mass images with different fracture types as examples,the identification results show that the proposed algorithm can accurately identify the multiform fractures,which lays the foundation for calculating the mechanical parameters of rock masses.
In a mathematical program with generalized complementarity constraints(MPGCC),complementarity relation is imposed between each pair of variable *** includes the traditional mathematical program with complementarity co...
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In a mathematical program with generalized complementarity constraints(MPGCC),complementarity relation is imposed between each pair of variable *** includes the traditional mathematical program with complementarity constraints(MPCC)as a special *** account of the disjunctive feasible region,MPCC and MPGCC are generally difficult to *** l_(1)penalty method,often adopted in computation,opens a way of circumventing the *** it remains unclear about the exactness of the l_(1)penalty function,namely,whether there exists a sufficiently large penalty parameter so that the penalty problem shares the optimal solution set with the original *** this paper,we consider a class of MPGCCs that are of multi-affine objective *** problem class finds applications in various fields,e.g.,the multi-marginal optimal transport problems in many-body quantum physics and the pricing problems in network *** first provide an instance from this class,the exactness of whose l_(1)penalty function cannot be derived by existing *** then establish the exactness results under rather mild *** results cover those existing ones for MPCC and apply to multi-block contexts.
We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic ***,we propose a specific algorithm termed STRME,in which the trust-region radius depends linearly on the ...
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We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic ***,we propose a specific algorithm termed STRME,in which the trust-region radius depends linearly on the gradient used to define the latest *** complexity results of the STRME method in nonconvex,convex and strongly convex settings are presented,which match those of the existing algorithms based on probabilistic *** addition,several numerical experiments are carried out to reveal the benefits of the proposed methods compared to the existing stochastic trust-region methods and other relevant stochastic gradient methods.
The proximal alternating linearized minimization(PALM)method suits well for solving blockstructured optimization problems,which are ubiquitous in real *** the cases where subproblems do not have closed-form solutions,...
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The proximal alternating linearized minimization(PALM)method suits well for solving blockstructured optimization problems,which are ubiquitous in real *** the cases where subproblems do not have closed-form solutions,e.g.,due to complex constraints,infeasible subsolvers are indispensable,giving rise to an infeasible inexact PALM(PALM-I).Numerous efforts have been devoted to analyzing the feasible PALM,while little attention has been paid to the *** usage of the PALM-I thus lacks a theoretical *** essential difficulty of analysis consists in the objective value nonmonotonicity induced by the *** study in the present work the convergence properties of the *** particular,we construct a surrogate sequence to surmount the nonmonotonicity issue and devise an implementable inexact *** upon these,we manage to establish the stationarity of any accumulation point,and moreover,show the iterate convergence and the asymptotic convergence rates under the assumption of the Lojasiewicz *** prominent advantages of the PALM-I on CPU time are illustrated via numerical experiments on problems arising from quantum physics and 3-dimensional anisotropic frictional contact.
In this paper,we develop a new sixth-order WENO scheme by adopting a convex combina-tion of a sixth-order global reconstruction and four low-order local *** the classical WENO schemes,the associated linear weights of ...
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In this paper,we develop a new sixth-order WENO scheme by adopting a convex combina-tion of a sixth-order global reconstruction and four low-order local *** the classical WENO schemes,the associated linear weights of the new scheme can be any positive numbers with the only requirement that their sum equals ***,a very simple smoothness indicator for the global stencil is *** new scheme can achieve sixth-order accuracy in smooth *** tests in some one-and two-dimensional bench-mark problems show that the new scheme has a little bit higher resolution compared with the recently developed sixth-order WENO-Z6 scheme,and it is more efficient than the classical fifth-order WENO-JS5 scheme and the recently developed sixth-order WENO6-S scheme.
1 Introduction In recent years,the Massively Parallel Computation(MPC)model has gained significant ***,most of distributed and parallel graph algorithms in the MPC model are designed for static graphs[1].In fact,the g...
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1 Introduction In recent years,the Massively Parallel Computation(MPC)model has gained significant ***,most of distributed and parallel graph algorithms in the MPC model are designed for static graphs[1].In fact,the graphs in the real world are constantly *** size of the real-time changes in these graphs is smaller and more *** graph algorithms[2,3]can deal with graph changes more efficiently[4]than the corresponding static graph ***,most studies on dynamic graph algorithms are limited to the single machine ***,a few parallel dynamic graph algorithms(such as the graph connectivity)in the MPC model[5]have been proposed and shown superiority over their parallel static counterparts.
The new concept"derimorphism"generalizing both derivation and homomor-phism is *** a derimorphism is invertible,its inverse is a Rota-Baxter *** general theory of derimorphism is *** classification of all de...
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The new concept"derimorphism"generalizing both derivation and homomor-phism is *** a derimorphism is invertible,its inverse is a Rota-Baxter *** general theory of derimorphism is *** classification of all derimorphisms over an associative unital algebra is *** to the nonexistence of nontriv-ial positive derivations,it is shown that nontrivial positive derimorphisms do exist over any pair of opposite orderings over R[x],the lattice-ordered full matrix algebra and upper triangular matrix algebra over a totally ordered field.
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