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Feasible directions linear programming by neural networks

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Feasible directions linear programming by neural networks

1990 International Joint Conference on Neural Networks - IJCNN 90 Part 3 (of 3)

作者： Barbosa, Valmir C. de Carvalho, Luis Alfredo V. COPPE Univ Fed do Rio de Janeiro Brazil

The authors describe how a neural network can be built for the exact solution of linear programming problems by a feasible directions approach. The proposed network, when started at any interior point, continuously tracks a path of equally interior points converging to an optimal solution. The number of neurons in the network grows linearly with the problem size, and neurons are relatively sparsely connected. Initial simulation results indicate that convergence is very fast, and consequently the network can be of relevance to many application areas.

关键词： mathematical programming, linear

Applications of the AT&T KORBX systems for the petroleum industry

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Applications of the AT&T KORBX systems for the petroleum ind...

Proceedings of the ISA '90 International Conference and Exhibition Part 3 (of 4)

作者： Ikura, Yoshiro AT&T Advanced Decision Support Systems Berkeley Heights United States

In 1984, a mathematical breakthrough in linear programming was announced by a young scientist, Narendra Karmarkar, at AT&T Bell Laboratories. This new method enables major industries and government organizations to quickly optimize operations and planning problems which were considered practically intractable before. AT&T's new business unit, Advanced Decision Support Systems, has developed a system, the AT&T KORBX System, based on this invention. It has successfully applied it to complex industry decision problems. We present applications of this technology to oil industry problems, and show benchmark results using real data. In particular, refinery operations planning and scheduling problems will be discussed together with potential benefits obtainable from this new system.

关键词： mathematical programming, linear

Facet identification for the symmetric traveling salesman polytope

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mathematical programming, Series A 1990年第2期47卷 219-257页

作者： Padberg, Manfred Rinaldi, Giovanni New York Univ United States

Several procedures for the identification of facet inducing inequalities for the symmetric traveling salesman polytope are given. An identification procedure accepts as input the support graph of a point which does not belong to the polytope, and returns as output some of the facet inducing inequalities violated by the point. A procedure which always accomplishes this task is called exact, otherwise it is called heuristic. We give exact procedures for the subtour elimination and the 2-matching constraints, based on the Gomory-Hu and Padberg-Rao algorithms respectively. Efficient reduction procedures for the input graph are proposed which accelerate these two algorithms substantially. Exact and heuristic shrinking conditions for the input graph are also given that yield efficient procedures for the identification of simple and general comb inequalities and of some elementary clique tree inequalities. These procedures constitute the core of a polytopal cutting plane algorithm that we have devised and programmed to solve a substantial number of large-scale problem instances with sizes up to 2392 nodes to optimality.

关键词： mathematical programming, linear

Relaxation methods for monotropic programs

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mathematical programming, Series A 1990年第2期46卷 127-151页

作者： Tseng, Paul Bertsekas, Dimitri P. Massachusetts Inst of Technology United States

We propose a dual descent method for the problem of minimizing a convex, possibly nondifferentiable, separable cost subject to linear constraints. The method has properties reminiscent of the Gauss-Seidel method in numerical analysis and uses the Ε-complementary slackness mechanism introduced by D.P. Bertsekas, P.A. Hosein and P. Tseng to ensure finite convergence to near optimality. As special cases we obtain the methods of Bertsekas et al. for network flow programs and the methods in P. Tseng and D.P. Bertsekas for linear programs.

关键词： mathematical programming, linear

An algorithm for linear programming which requires O(((m+n)n2+(m+n)1.5n)L) arithmetic operations

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mathematical programming, Series A 1990年第2期47卷 175-201页

作者： Vaidya, Pravin M. AT&T Bell Lab United States

We present an algorithm for linear programming which requires O(((m+n)n2+(m+n)1.5n)L) arithmetic operations where m is the number of constraints, and n is the number of variables. Each operation is performed to a precision of O(L) bits. L is bounded by the number of bits in the input. The worst-case running time of the algorithm is better than that of Karmarkar's algorithm by a factor of √m+n.

关键词： mathematical programming, linear

Interative algorithm for solving the linear programming problem

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Soviet journal of automation and information sciences

Soviet journal of automation and information sciences 1990年第1期23卷 41-52页

作者： Lychak, M.M. Glushkov Cybernetics Inst UkrSSR Acad of Sciences Russia

An interative algorithm for solving a variant of the linear programming is proposed with geometrical representation of formation of polyhedral sets in the space of variables. The algorithm is based on the clipping met... 详细信息

关键词： mathematical programming, linear

Asymptotic behaviour of Karmarkar's method for linear programming

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mathematical programming, Series A 1990年第2期46卷 173-190页

作者： Asic, Miroslav D. Kovacevic-Vujcic, Vera V. Radosavljevic-Nikolic, Mirjana D. Ohio State Univ United States

The asymptotic behaviour of Karmarkar's method is studied and an estimate of the rate of the objective function value decrease is given. Two possible sources of numerical instability are discussed and a stabilizin... 详细信息

关键词： mathematical programming, linear

Mixed integer linear bilevel programming problem

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Operations Research 1990年第5期38卷 911-921页

作者： Moore, James T. Bard, Jonathan F. Offutt Air Force Base Omaha United States

A two-person, noncooperative game in which the players move in sequence can be modeled as a bilevel optimization problem. In this paper, we examine the case where each player tries to maximize the individual objective function over a jointly constrained polyhedron. The decision variables are variously partitioned into continuous and discrete sets. The leader goes first, and through his choice may influence but not control the responses available to the follower. For two reasons the resultant problem is extremely difficult to solve, even by complete enumeration. First, it is not possible to obtain tight upper bounds from the natural relaxation;and second, two of the three standard fathoming rules common to branch and bound cannot be applied fully. In light of these limitations, we develop a basic implicit enumeration scheme that finds good feasible solutions within relatively few iterations. A series of heuristics are then proposed in an effort to strike a balance between accuracy and speed. The computational results suggest that some compromise is needed when the problem contains more than a modest number of integer variables.

关键词： mathematical programming, linear

Empirical evaluation of the KORBX algorithms for military airlift applications

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Operations Research 1990年第2期38卷 240-248页

作者： Carolan, William J. Hill, James E. Kennington, Jeffery L. Niemi, Sandra Wichmann, Stephen J. HQ MAC/AG United States

KORBX (a registered trademark of AT&T) is AT&T's new system for solving large-scale linear programs. The system consists of both hardware, which uses parallel processing technology configured with 256 MB of memory, and software which exploits the design and resources of this modern hardware. The KORBX linear programming software system contains four algorithms which are variations of the interior point method of Narendra Karmarkar. The primal, dual, primal-dual, and power series algorithms were empirically evaluated on a set of linear programming application models being used by the staff of the Military Airlift Command at Scott Air Force Base. For calibration purposes, a set of smaller test problems were also run using MPSX and XMP;and some pure network problems were solved using NETFLO, MPSX, and XMP.

关键词： mathematical programming, linear