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Optimality conditions and DC-Dinkelbach-type algorithm for vector fractional programming problems with ratios of difference of convex functions

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OPTIMIZATION 2025年第2期74卷 427-457页

作者： Ghazi, A. Roubi, A. Hassan First Univ Fac Sci Tech Lab MISI Settat Morocco

\In this work, necessary optimality conditions of KKT type for (weak) Pareto optimality are derived and a DC-Dinkelbach-type algorithm is proposed for vector fractional mathematical programs with ratios of difference of convex (DC) functions, and DC constraints, by reducing the latter to a system of scalar parametric problems and using DC tools. The special case of vector fractional programs with ratios of convex functions is also analysed.

关键词： vector programming fractional programming difference of convex functions optimality conditions Dinkelbach algorithm

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Computational enhancements in low-rank semidefinite programming

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OPTIMIZATION METHODS & SOFTWARE 2006年第3期21卷 493-512页

作者： Burer, S Choi, C Univ Iowa Iowa City IA 52242 USA

We discuss computational enhancements for the low-rank semidefinite programming algorithm, including the extension to block semidefinite programs (SDPs), an exact linesearch procedure, and a dynamic rank reduction scheme. A truncated-Newton method is also introduced, and several preconditioning strategies are proposed. Numerical experiments illustrating these enhancements are provided on a wide class of test problems. In particular, the truncated-Newton variant is able to achieve high accuracy in modest amounts of time on maximum-cut-type SDPs.

关键词： semidefinite programming low-rank matrices vector programming non-linear programming numerical experiments

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Inelastic vector finite element analysis of RC shells

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STRUCTURAL ENGINEERING AND MECHANICS 1996年第2期4卷 139-148页

作者： Min, CS Gupta, AK N CAROLINA STATE UNIV CTR NUCL POWER PLANT STRUCT EQUIPMENT & PIPINGRALEIGHNC 27695

vector algorithms and the relative importance of the four basic modules (computation of element stiffness matrices, assembly of the global stiffness matrix, solution of the system of linear simultaneous equations, and calculation of stresses and strains) of a finite element computer program for inelastic analysis of reinforced concrete shells are presented. Performance of the vector program is compared with a scalar program. For a cooling tower problem, the speedup factor from the scalar to the vector program is 34 for the element stiffness matrices calculation, 25.3 for the assembly of global stiffness matrix, 27.5 for the equation solver, and 37.8 for stresses, strains and nodal forces computations on a Gray Y-MP. The overall speedup factor is 30.9. When the equation solver alone is vectorized, which is computationally the most intensive part of a finite element program, a speedup factor of only 1.9 is achieved. When the rest of the program is also vectorized, a large additional speedup factor of 15.9 is attained. Therefore, it is very important that all the modules in a nonlinear program are vectorized to gain the full potential of the supercomputers. The vector finite element computer program for inelastic analysis of RC shells with layered elements developed in the present study enabled us to perform mesh convergence studies. The vector program can be used for studying the ultimate behavior of RC shells and used as a design tool.

关键词： inelastic inelasticity nonlinear nonlinearity vector computer vector programming vector algorithm finite element method finite element analysis reinforced concrete shells

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Local minima and convergence in low-rank semidefinite programming

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MATHEMATICAL programming 2005年第3期103卷 427-444页

作者： Burer, S Monteiro, RDC Univ Iowa Dept Management Sci Iowa City IA 52242 USA Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

The low-rank semidefinite programming problem LRSDPr is a restriction of the semidefinite programming problem SDP in which a bound r is imposed on the rank of X, and it is well known that LRSDPr is equivalent to SDP if r is not too small. In this paper, we classify the local minima of LRSDPr and prove the optimal convergence of a slight variant of the successful, yet experimental, algorithm of Burer and Monteiro [5], which handles LRSDPr via the nonconvex change of variables X = RRT. In addition, for particular problem classes, we describe a practical technique for obtaining lower bounds on the optimal solution value during the execution of the algorithm. Computational results are presented on a set of combinatorial optimization relaxations, including some of the largest quadratic assignment SDPs solved to date.

关键词： semidefinite programming low-rank matrices vector programming combinatorial optimization nonlinear programming augmented Lagrangian numerical experiments

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Conic set-valued maps in vector optimization

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SET-VALUED ANALYSIS 2007年第1期15卷 47-59页

作者： Jimenez Guerra, Pedro Angel Melguizo, Miguel Munoz-Bouzo, Maria J. Univ Autonoma Madrid Fac Ciencias Dept Matemat Fundamentales UNED Madrid 28040 Spain Univ Alicante Dept Matemat Aplicada Alicante 03690 Spain

The paper deals with the properties of a conic set-valued function defined on the set of all ideal points of vector programming problems. The results here about the continuity and derivability of this conic set-valued map, can be used to get information about the sensitivity of the problem and the stability of the order associated to every ideal point. Furthermore, it is proved that certain contingent cones are determined by the ideal conic set-valued map.

关键词： ideal point conic set-valued map vector programming

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NumCIL and Bohrium: High Productivity and High Performance 11th

NumCIL and Bohrium: High Productivity and High Performance

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11th International Conference on Parallel Processing and Applied Mathematics (PPAM)

作者： Skovhede, Kenneth Lund, Simon Andreas Frimann Univ Copenhagen Niels Bohr Inst Copenhagen Denmark

ISBN: (纸本)9783319321523;9783319321516

In this paper, we explore the mapping of the NumCIL C# vector library where operations are offloaded to the Bohrium runtime system and evaluate the performance gains. By using a feature-rich language, such as C#, we argue that productivity can be increased. The use of the Bohrium runtime system allows all vector operations written in C# to be executed efficiently on multi-core systems. We evaluate the presented design through a setup that targets a 32 core machine. The evaluation includes well-known benchmark applications, such as Black Sholes, 5-point stencil, Shallow Water, and N-body.

关键词： C# NumCIL Bohrium High performance High productivity vector programming Array programming

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A Performance Optimization Framework for the Simultaneous Heterogeneous Computing Platforms

A Performance Optimization Framework for the Simultaneous He...

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ACM Workshop on Software Engineering Methods for Parallel and High Performance Applications (SEM4HPC)

作者： Li, Shuo Intel Corp 2111 NE 25th Ave Hillsboro OR 97124 USA

ISBN: (纸本)9781450343510

Heterogeneous computing platforms with multicore host system and many-core accelerator devices have taken a major step forward in the mainstream HPC computing market this year with the announcement of HP Apollo 6000 System's ProLiant XL250a server features the Intel (R) Xeon Phi (TM) coprocessors. Although many application developers attempt to use it in the same way as GPGPU acceleration platforms, doing so forfeits the processing capability of multicore host processors and introduces power inefficiency in business operations. In this paper, we propose an application optimization framework to turn sequential legacy applications into highly parallel applications that make use of the hardware resources both on the host CPU and on the accelerator devices to enable simultaneous heterogeneous computing. As a case study, we look at how to apply this framework and adopt a structured methodology to develop option pricing applications to take advantages of a heterogeneous computing environment.

关键词： programming Model Performance Measurement Many-core programming vector programming Development Tools application acceleration Power consumption multithreaded parallelism Heterogeneous programming

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