We present an interior-point penalty method for nonlinear programming (NLP), where the merit function consists of a piecewise linear penalty function and an a"" (2)-penalty function. The piecewise linear pen...
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We present an interior-point penalty method for nonlinear programming (NLP), where the merit function consists of a piecewise linear penalty function and an a"" (2)-penalty function. The piecewise linear penalty function is defined by a set of break points that correspond to pairs of values of the barrier function and the infeasibility measure at a subset of previous iterates and this set is updated at every iteration. The a"" (2)-penalty function is a traditional penalty function defined by a single penalty parameter. At every iteration the step direction is computed from a regularized Newton system of the first-order equations of the barrier problem proposed in Chen and Goldfarb (Math Program 108:1-36, 2006). Iterates are updated using a line search. In particular, a trial point is accepted if it provides a sufficient reduction in either of the penalty functions. We show that the proposed method has the same strong global convergence properties as those established in Chen and Goldfarb (Math Program 108:1-36, 2006). Moreover, our method enjoys fast local convergence. Specifically, for each fixed small barrier parameter mu, iterates in a small neighborhood (roughly within o(mu)) of the minimizer of the barrier problem converge Q-quadratically to the minimizer. The overall convergence rate of the iterates to the solution of the nonlinear program is Q-superlinear.
This paper presents a new practical algorithm (i.e. Projected Combination Direction Algorithm) for large scale optimization with simple bound constraints, and study some properties of this method, particularly, the gl...
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This paper presents a new practical algorithm (i.e. Projected Combination Direction Algorithm) for large scale optimization with simple bound constraints, and study some properties of this method, particularly, the global convergence property is shown. The numerical results are reported for 3 modified forms.
The optimum receiver to detect the bits of multiple code-divison multiple access (CDMA) users has exponential complexity in the number of active users in the system. Consequently, many suboptimum receivers have been d...
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The optimum receiver to detect the bits of multiple code-divison multiple access (CDMA) users has exponential complexity in the number of active users in the system. Consequently, many suboptimum receivers have been developed to achieve good performance with less complexity. In this paper, we take the approach of approximating the solution of the optimum multiuser detection problem (OMUD) using nonlinear programming relaxations. First, we observe that some popular suboptimum receivers indeed correspond to relaxations of the optimal detection problem. In particular, one proposed approximation method yields to iterative solutions which correspond to previously proposed heuristic nonlinear detectors. Using a nonlinear programming approach, we identify the convergence properties of these iterative detectors. Secondly, we propose a relaxation that yields a receiver which we call the generalized minimum mean squared error detector. We give a simple iterative implementation of the detector. Its performance is evaluated and comparisons to other suboptimum detection schemes are given.
We introduce a framework in which updating rules for the barrier parameter in primal-dual interior-point methods become dynamic. The original primal-dual system is augmented to incorporate explicitly an updating funct...
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We introduce a framework in which updating rules for the barrier parameter in primal-dual interior-point methods become dynamic. The original primal-dual system is augmented to incorporate explicitly an updating function. A Newton step for the augmented system gives a primal-dual Newton step and also a step in the barrier parameter. Based on local information and a line search, the decrease of the barrier parameter is automatically adjusted. We analyze local convergence properties, report numerical experiments on a standard collection of nonlinear problems and compare our results to a state-of-the-art interior-point implementation. In many instances, the adaptive algorithm reduces the number of iterations and of function evaluations. Its design guarantees a better fit between the magnitudes of the primal-dual residual and of the barrier parameter along the iterations.
The VIKOR method was introduced as a Multi-Attribute Decision Making (MADM) method to solve discrete decision-making problems with incommensurable and conflicting criteria. This method focuses on ranking and selecting...
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The VIKOR method was introduced as a Multi-Attribute Decision Making (MADM) method to solve discrete decision-making problems with incommensurable and conflicting criteria. This method focuses on ranking and selecting from a set of alternatives based on the particular measure of "closeness" to the "ideal" solution. The multi-criteria measure for compromise ranking is developed from the l-p metric used as an aggregating function in a compromise programming method. In this paper, the VIKOR method is extended to solve Multi-Objective Large-Scale Non-Linear programming (MOLSNLP) problems with block angular structure. In the proposed approach, the Y-dimensional objective space is reduced into a one-dimensional space by applying the Dantzig-Wolfe decomposition algorithm as well as extending the concepts of VIKOR method for decision-making in continues environment. Finally, a numerical example is given to illustrate and clarify the main results developed in this paper.
作者：
Chen, ZWHan, JYXu, DCSuzhou Univ
Dept Math Suzhou 215006 Jingsu Province Peoples R China Chinese Acad Sci
Acad Math & Syst Sci Inst Appl Math Beijing 100080 Peoples R China Chinese Acad Sci
Acad Math & Syst Sci Inst Computat Math & Sci Engn Comp Beijing 100080 Peoples R China
In this paper we propose a nonmonotone trust region algorithm for optimization with simple bound constraints. Under mild conditions, we prove the global convergence of the algorithm. For the monotone case it is also p...
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In this paper we propose a nonmonotone trust region algorithm for optimization with simple bound constraints. Under mild conditions, we prove the global convergence of the algorithm. For the monotone case it is also proved that the correct active set can be identified in a finite number of iterations if the strict complementarity slackness condition holds, and so the proposed algorithm reduces finally to an unconstrained minimization method in a finite number of iterations, allowing a fast asymptotic rate of convergence. Numerical experiments show that the method is efficient.
We show that indefinitely preconditioned symmetric Krylov-subspace methods are very efficient for solving linearized KKT systems arising in equality constrained optimization. We give a numerical comparison of various ...
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We show that indefinitely preconditioned symmetric Krylov-subspace methods are very efficient for solving linearized KKT systems arising in equality constrained optimization. We give a numerical comparison of various Krylov subspace methods in three different forms (original system, null-space transformation, range-space transformation). Furthermore, we give a survey of our previous results concerning indefinite preconditioners and merit functions and prove new propositions.
This paper presents a numerical upper bound limit analysis using radial point interpolation method (RPIM) and a direct iterative method with nonlinear programming. By expressing the internal plastic dissipation power ...
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This paper presents a numerical upper bound limit analysis using radial point interpolation method (RPIM) and a direct iterative method with nonlinear programming. By expressing the internal plastic dissipation power with a kinematically admissible velocity field obtained through RPIM interpolation, the upper bound problem is formulated mathematically as a nonlinear programming subjected to single equality constraint which is solved by a direct iterative method. To evaluate the integration of internal power dissipation rate without any background integral cell, a new meshless integration technique based on Cartesian Transformation Method (CTM) is employed to transform the domain integration first as boundary integration and then one-dimensional integration. The effectiveness and accuracy of the proposed approach are demonstrated by two classical limit analysis problems. Further discussion is devoted to optimal selection of relevant parameters for the computation. (C) 2013 Published by Elsevier Ltd.
A new method is described for the determination of optimal spacecraft trajectories in an inverse-square field using finite, fixed thrust. The method employs a recently developed direct optimization technique that uses...
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A new method is described for the determination of optimal spacecraft trajectories in an inverse-square field using finite, fixed thrust. The method employs a recently developed direct optimization technique that uses a piecewise polynomial representation for the state and controls and collocation, thus converting the optimal control problem into a nonlinear programming problem, which is solved numerically. This technique has been modified to provide efficient handling of those portions of the trajectory that can be determined analytically, i.e., the coast arcs. Among the problems that have been solved using this method are optimal rendezvous and transfer (including multirevolution cases) and optimal multiburn orbit insertion from hyperbolic approach.
The existence of second-order sufficient conditions (SOSCs) for nonlinear programming problems is an interesting theoretical result. It is not, however, immediately clear how one might use them in practice to determin...
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The existence of second-order sufficient conditions (SOSCs) for nonlinear programming problems is an interesting theoretical result. It is not, however, immediately clear how one might use them in practice to determine if a candidate point produced by an algorithm operating on an actual problem is indeed optimal. We present a simple method for computationally checking the SOSCs (for the case when the Karush-Kuhn-Tucker (KKT) multipliers for all active inequality constraints are positive) in a finite number of steps that at once sheds light on their meaning and provides a computational tool for use in checking the results produced by algorithms on actual problems. Furthermore, this method serves as a nice bridge from a class on the theory of nonlinear programming to one on algorithms, as it connects the SOSCs to the conjugate structure of a problem, a concept important in the construction of many solution methods.
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