A very surprising result is derived in this paper, that there exists a family of LP duals for general NLP problems. A general dual problem is first derived from implied constraints via a simple bounding technique. It ...
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A very surprising result is derived in this paper, that there exists a family of LP duals for general NLP problems. A general dual problem is first derived from implied constraints via a simple bounding technique. It is shown that the Lagrangian dual is a special case of this general dual and that other special cases turn out to be LP problems. The LP duals provide a very powerful computational device but are derived using fairly strict conditions. Hence, they can often be infeasible even if the primal NLP problem is feasible and bounded. Many directions for relaxing these conditions are outlined for future research. A concept of local duality is also introduced for the first time akin to the concept of local optimality. (C) 1999 Elsevier Science B.V. All rights reserved.
This paper deals with the identification of a linear parameter-varying (LPV) system whose parameter dependence can be written as a linear/fractional transformation (LFT). We formulate an output-error identification pr...
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This paper deals with the identification of a linear parameter-varying (LPV) system whose parameter dependence can be written as a linear/fractional transformation (LFT). We formulate an output-error identification problem and present a parameter estimation scheme in which a prediction error-based cost function is minimized using nonlinear programming;its gradients and (approximate) Hessians can be completed using LPV fillers and inner products, and identifiable model sets (i.e., local canonical forms) are obtained efficiently using a natural geometrical approach. Some computational issues and experiences are discussed, and a simple numerical example is provided for illustration.
A collaboration planning model (CPM) for co-ordination of supply chain (SC) is established by the sharing of information, based on up and downstream planning models respectively. The factors under internal as well as ...
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A collaboration planning model (CPM) for co-ordination of supply chain (SC) is established by the sharing of information, based on up and downstream planning models respectively. The factors under internal as well as external situations (price, inventory etc.) are considered in the model. The relationship of cooperating partnership is determined, and the goal of win-win is obtained by negotiation theory. Experiments using realistic data from enterprises have achieved satisfactory results.
An interior trust-region-based algorithm for linearly constraind minimization problems is proposed and analyzed. This algorithm is similar to trust region algorithms for unconstrained minimization: a trust region subp...
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An interior trust-region-based algorithm for linearly constraind minimization problems is proposed and analyzed. This algorithm is similar to trust region algorithms for unconstrained minimization: a trust region subproblem on a subspace is solved in each iteration. We establish that the proposed algorithm has convergence properties analogous to those of the generated sequence satisfies to Krush-Kuhn-Tucker (KKT) conditions and at least one limit point satisfies second order necessary optimality conditions. In addition, if one limit point is a strong local minimizer and the Hessian is Lipschitz continuous in a neighborhood of that point, then the generated sequence converges globally to that point in the rate of at least 2-step quadratic. We are mainly concerned sequence converges globally to that point in the rate of at least 2-step quadratic. We are mainly concerned with the theoretical properties of the algorithm.
A method of optimizing high-performance concrete mix proportioning for a given workability and compressive strength using artificial neural networks and nonlinear programming is described. The basic procedure of the m...
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A method of optimizing high-performance concrete mix proportioning for a given workability and compressive strength using artificial neural networks and nonlinear programming is described. The basic procedure of the methodology consists of three steps: (1) Build accurate models for workability and strength using artificial neural networks and experimental data;(2) incorporate these models in software allowing an evaluation of the specified properties for a given mix;and (3) incorporate the software in a nonlinear programming package allowing a search of the optimum proportion mix design. For performing optimum concrete mix design based on the proposed methodology, a software package has been developed. One can conduct mix simulations covering all the important properties of the concrete at the same time. To demonstrate the utility of the proposed methodology, experimental results from several different mix proportions based on various design requirements are presented.
As an outgrowth of our investigation of non-regular spaces within the context of quantum gravity and non-commutative geometry, we develop a graph Hilbert space framework on arbitrary (infinite) graphs and use it to st...
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As an outgrowth of our investigation of non-regular spaces within the context of quantum gravity and non-commutative geometry, we develop a graph Hilbert space framework on arbitrary (infinite) graphs and use it to study spectral properties of graph Laplacians and graph Dirac operators. We define a spectral triplet sharing most of the properties of what Connes calls a spectral triple. With the help of this scheme we derive an explicit expression for the Connes-distance function on general directed or undirected graphs. We derive a series of a priori estimates and calculate it for a variety of examples of graphs. As a possibly interesting side, we show that the natural setting for approaching such problems may be the framework of (non) linear programming or optimization. We compare our results (arrived at within our particular framework) with those of other authors and show that the seeming differences depend on the use of different graph geometries and/or Dirac operators.
We extend the numerical embedding method for solving the smooth equations to the nonlinear complementarity problem. By using the nonsmooth theory, we prove the existence and the continuation of the follow the path for...
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We extend the numerical embedding method for solving the smooth equations to the nonlinear complementarity problem. By using the nonsmooth theory, we prove the existence and the continuation of the follow the path for the corresponding homotopy equations. Therefore the basic theory of the numerical embedding method for solving the nonlinear complementarity problem is established. In part II of this paper, we will further study the implementation of the method and give some numerical examples.
A P*-nonlinear Complementarity Problem as a generalization of the P*Linear Complementarity Problem is considered. We show that the long-step version of the homogeneous self-dual interior-point algorithm could be used ...
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A P*-nonlinear Complementarity Problem as a generalization of the P*Linear Complementarity Problem is considered. We show that the long-step version of the homogeneous self-dual interior-point algorithm could be used to solve such a problem. The algorithm achieves linear global convergence and quadratic local convergence under the following assumptions: the function satisfies a modified scaled Lipschitz condition, the problem has a strictly complementary solution, and certain submatrix of the Jacobian is nonsingular on some compact set.
The design and implementation of a new algorithm for solving large nonlinear programming problems is described. It follows a barrier approach that employs sequential quadratic programming and trust regions to solve th...
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The design and implementation of a new algorithm for solving large nonlinear programming problems is described. It follows a barrier approach that employs sequential quadratic programming and trust regions to solve the subproblems occurring in the iteration. Both primal and primal-dual versions of the algorithm are developed, and their performance is illustrated in a set of numerical tests.
Lower-bound estimates for the ground-state energy of the helium atom are determined using nonlinear programming techniques. Optimized lower bounds are determined for single-particle, radially correlated, and general c...
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Lower-bound estimates for the ground-state energy of the helium atom are determined using nonlinear programming techniques. Optimized lower bounds are determined for single-particle, radially correlated, and general correlated wave functions. The local nature of the method employed makes it a very severe test of the accuracy of the wave function. (C) 1999 John Wiley & Sons, Inc.
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