Sparse sequential quadratic programming (SQP) has offered fast and robust convergence of trajectory optimization based on direct collocation. However, the conventional approach of calculating the Hessian of the Lagran...
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Sparse sequential quadratic programming (SQP) has offered fast and robust convergence of trajectory optimization based on direct collocation. However, the conventional approach of calculating the Hessian of the Lagrangian is sometimes inefficient in view of the computational time. Therefore, this paper proposes two novel Hessian calculation methods that exploit the doubly-bordered block diagonal structure of the Hessian. Through applications to the constrained brachistochrone problem and the space shuttle reentry problem, the proposed methods were demonstrated to show faster convergence speeds as compared with the conventional methods.
In this comments paper, we revisit the network model introduced in [1]. We discuss the inaccuracy of the model and, to correct the network model, we propose to apply directed capacity constraints for directed flows. B...
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In this comments paper, we revisit the network model introduced in [1]. We discuss the inaccuracy of the model and, to correct the network model, we propose to apply directed capacity constraints for directed flows. Based on a comparison of numerical results, we show that the corrected model leads to better accuracy than the original model.
In this study, the performance of the modified subgradient algorithm (MSG) to solve the 0-1 quadratic knapsack problem (QKP) is examined. The MSG is proposed by Gasimov for solving dual problems constructed with respe...
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ISBN:
(纸本)9789955282839
In this study, the performance of the modified subgradient algorithm (MSG) to solve the 0-1 quadratic knapsack problem (QKP) is examined. The MSG is proposed by Gasimov for solving dual problems constructed with respect to sharp Augmented Lagrangian function. The MSG has some important proven properties. For example, it is convergent, and it guarantees the zero duality gap for the problems such that its objective and constraint functions are all Lipschtz. Besides it doesn't need to be convexity or differentiability conditions on the primal problem. The MSG has successfully used for solving nonconvex continuous and some combinatorial problems with equality constraints since it was suggested. In this study, the MSG is used to solve the QKP which is one of the well known combinatorial optimization problems with inequality constraint. Firstly, zero-one nonlinear problem is converted into continuous nonlinear problem by adding only one constraint and not adding new variables, then to solve the continuous QKP, dual problem with "zero duality gap" is constructed by using the sharp Augmented Lagrangian function. Finally, to solve the dual problem, the MSG is used by considering the equality constraint in the computation of the norm. The proposed approach is applied for some test problems. The results are also presented and discussed.
Four step (sequential) procedures are traditionally used in forecasting travel on an urban transportation network. A typical transportation network consists of different trip purposes, user classes, and transportation...
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ISBN:
(纸本)9789889884734
Four step (sequential) procedures are traditionally used in forecasting travel on an urban transportation network. A typical transportation network consists of different trip purposes, user classes, and transportation modes. Due to the inconsistency results from the four step procedures, some research works proposed to combine these four step procedures. The resulting transportation model becomes a quite general supply-demand equilibrium problem which is a class of variational inequalities with a small number of asymmetric functions (also called combined model). Hence, we propose that Dantzig-Wolfe decomposition method should be used to divide the model into a small-scale equilibrium problem (variational inequalities) with the asymmetric functions and a large-scale symmetric transportation model (a nonlinear programming) with all of the details of network structure and trip demand.
In this paper I describe a new and exciting application of optimization technology. The problem is to design a space telescope capable of imaging Earth-like planets around nearby stars. Because of limitations inherent...
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In this paper I describe a new and exciting application of optimization technology. The problem is to design a space telescope capable of imaging Earth-like planets around nearby stars. Because of limitations inherent in the wave nature of light, the design problem is one of diffraction control so as to provide the extremely high contrast needed to image a faint planet positioned very close to its much brighter star. I will describe the mathematics behind the diffraction control problem and explain how modern optimization tools were able to provide unexpected solutions that actually changed NASA's approach to this problem.
Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is pr...
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Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.
The aim of the paper is to show how to explicitly express the function of sectional curvature with the first and second derivatives of the problem's functions in the case of submanifolds determined by equality con...
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The aim of the paper is to show how to explicitly express the function of sectional curvature with the first and second derivatives of the problem's functions in the case of submanifolds determined by equality constraints in the n-dimensional Euclidean space endowed with the induced Riemannian metric, which is followed by the formulation of the minimization problem of sectional curvature at an arbitrary point of the given submanifold as a global minimization one on a Stiefel manifold. Based on the results, the sectional curvatures of Stiefel manifolds are analysed and the maximal and minimal sectional curvatures on an ellipsoid are determined.
Recently, a new Pattern Recognition technique based oil straight line segments (SLSs) was presented. The key issue in this new technique is to find a function based on distances between points and two sets of SLSs tha...
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ISBN:
(纸本)9780769533582
Recently, a new Pattern Recognition technique based oil straight line segments (SLSs) was presented. The key issue in this new technique is to find a function based on distances between points and two sets of SLSs that minimizes a certain error or risk criterion. An algorithm for solving this optimization problem is called training algorithm. Although this technique seems to be very promising, the first presented training algorithm is based on a heuristic. In fact, the search for this best function is a hard nonlinear optimization problem. In this paper we present a new and improved training algorithm for the SLS technique based on gradient descent optimization method. We have applied this new training algorithm to artificial and public data sets and their results confirm the improvement of this methodology.
In this paper, we develop heuristics for finding good starting points when solving large-scale nonlinear constrained optimization problems (COPS) formulated as nonlinear programming (NLP) and mixed-integer NLP (MINLP)...
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ISBN:
(纸本)9783540886358
In this paper, we develop heuristics for finding good starting points when solving large-scale nonlinear constrained optimization problems (COPS) formulated as nonlinear programming (NLP) and mixed-integer NLP (MINLP). By exploiting the localities of constraints, we first partition each problem by parallel decomposition into subproblems that are related by complicating constraints and complicating variables. We develop heuristics for finding good starting points that are critical for resolving the complicating constraints and variables. In our experimental evaluations of 255 benchmarks, our approach can solve 89.4% of the problems, whereas the best existing solvers can only solve 42.8%.
In most engineering applications, solutions derived from the lower bound theorem of limit analysis are particularly valuable because they provide a safe estimate of the load that will cause collapse. In this paper, th...
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ISBN:
(纸本)9780878493999
In most engineering applications, solutions derived from the lower bound theorem of limit analysis are particularly valuable because they provide a safe estimate of the load that will cause collapse. In this paper, the lower bound theorem is firstly implemented making use of the meshless local Petrov-Galerkin (MLPG) method with natural neighbour interpolation. In the present MLPG formulation, the natural neighbour interpolation is employed for constructing trial functions, while the three-node triangular FEM shape function is used as the test function over a local sub-domain. The self-equilibrium stress field is expressed by linear combination of several self-equilibrium stress basis vectors with parameters to be determined. These self-equilibrium stress basis vectors can be generated by performing an equilibrium iteration procedure during elasto-plastic incremental analysis. The Complex method is used to solve these nonlinear programming sub-problems and determine the maximal load amplifier. The numerical results show that the present solution procedure for limit analysis is effective and accurate.
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