In this paper a linear programming-based optimization algorithm called the Sequential Cutting Plane algorithm is presented. The main features of the algorithm are described, convergence to a Karush-Kuhn-Tucker station...
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In this paper a linear programming-based optimization algorithm called the Sequential Cutting Plane algorithm is presented. The main features of the algorithm are described, convergence to a Karush-Kuhn-Tucker stationary point is proved and numerical experience on some well-known test sets is showed. The algorithm is based on an earlier version for convex inequality constrained problems, but here the algorithm is extended to general continuously differentiable nonlinear programming problems containing both nonlinear inequality and equality constraints. A comparison with some existing solvers shows that the algorithm is competitive with these solvers. Thus, this new method based on solving linear programming subproblems is a good alternative method for solving nonlinear programming problems efficiently. The algorithm has been used as a subsolver in a mixed integer nonlinear programming algorithm where the linear problems provide lower bounds on the optimal solutions of the nonlinear programming subproblems in the branch and bound tree for convex, inequality constrained problems. (C) 2009 Elsevier B.V. All rights reserved.
This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of p...
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This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of points generated by this nonlinear La- grange algorithm is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions, and the error bound of solution, depending on the penalty parameter, is also established. It is shown that the condition number of the nonlinear Lagrangian Hessian at the optimal solution is proportional to the controlling penalty parameter. Moreover, the paper develops the dual algorithm associ- ated with the proposed nonlinear Lagrangians. Numerical results reported suggest that the dual algorithm based on proposed nonlinear Lagrangians is effective for solving some nonlinear optimization problems.
Particle swarm optimization (PSO) is an optimization technique based on population, which has similarities to other evolutionary algorithms. It is initialized with a population of random solutions and searches for opt...
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Particle swarm optimization (PSO) is an optimization technique based on population, which has similarities to other evolutionary algorithms. It is initialized with a population of random solutions and searches for optima by updating generations. Particle swarm optimization has become the hotspot of evolutionary computation because of its excellent performance and simple implementation. After introducing the basic principle of the PSO, a particle swarm optimization algorithm embedded with constraint fitness priority-based ranking method is proposed in this paper to solve nonlinear programming problem. By designing the fitness function and constraints-handling method, the proposed PSO can evolve with a dynamic neighborhood and varied inertia weighted value to find the global optimum. The results from this preliminary investigation are quite promising and show that this algorithm is reliable and applicable to almost all of the problems in multiple-dimensional, nonlinear and complex constrained programming. It is proved to be efficient and robust by testing some example and benchmarks of the constrained nonlinear programming problems. (c) 2005 Elsevier Ltd. All rights reserved.
Generalized fuzzy c-means (GFCM) is an extension of fuzzy c-means using L-p-norm distances. However, existing methods cannot solve GFCM with m = 1. To solve this problem, we define a new kind of clustering models, cal...
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Generalized fuzzy c-means (GFCM) is an extension of fuzzy c-means using L-p-norm distances. However, existing methods cannot solve GFCM with m = 1. To solve this problem, we define a new kind of clustering models, called L p-norm probabilistic K-means (L-p-PKM). Theoretically, L p-PKM is equivalent to GFCM at m = 1, and can have nonlinear programming solutions based on an efficient active gradient projection (AGP) method, namely, inverse recursion maximum-step active gradient projection (IRMSAGP). On synthetic and UCI datasets, experimental results show that L p-PKM performs better than GFCM (m > 1) in terms of initialization robustness, p-influence, and clustering performance, and the proposed IRMSAGP also achieves better performance than the traditional AGP in terms of convergence speed.
In the context of sequential methods for solving general nonlinear programming problems, it is usual to work with augmented subproblems instead of the original ones. This paper addresses the theoretical reasoning behi...
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In the context of sequential methods for solving general nonlinear programming problems, it is usual to work with augmented subproblems instead of the original ones. This paper addresses the theoretical reasoning behind handling the original subproblems by an augmentation strategy related to the differentiable reformulation of the-penalized problem. Nevertheless, this paper is not concerned with the sequential method itself, but with the features about the original problem that can be inferred from the properties of the solution of the augmented problem. Moreover, no assumption is made upon the feasibility of the original problem, neither about the fulfillment of any constraint qualification, nor of any regularity condition, such as calmness. The convergence analysis of the involved sequences is presented, independent of the strategy employed to produce the iterates. Examples that elucidate the interrelations among the obtained results are also provided.
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.
Riveted joints are expected to satisfy the requirements of strength, tightness, stiffness and in some cases heat and electric conductivity. Furthermore, the production time and cost should be minimal. Conventional des...
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Riveted joints are expected to satisfy the requirements of strength, tightness, stiffness and in some cases heat and electric conductivity. Furthermore, the production time and cost should be minimal. Conventional design procedures are effectively iterative techniques whose length and results are mainly dependent on designer intuition and experience. The design procedure in many cases is terminated when a feasible, however rarely the best, solution is reached. In this paper, an optimization procedure which eliminates the trial and error approach, is developed. This procedure determines the riveted joint configuration that minimizes production costs while satisfying stress and dimensional constraints. The calculation method which is based on non-linear programming techniques, is successfully applied to the rivited joints of two braking systems.
The paper addresses continuous-time nonlinear programming problems with equality and inequality constraints. First and second order necessary optimality conditions are obtained under a constant rank type constraint qu...
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The paper addresses continuous-time nonlinear programming problems with equality and inequality constraints. First and second order necessary optimality conditions are obtained under a constant rank type constraint qualification. The first order necessary conditions are of Karush-Kuhn-Tucker type.
This paper deals with a new variant of the inexact restoration method of Fischer and Friedlander (Comput Optim Appl 46:333-346, 2010) for nonlinear programming. We propose an algorithm that replaces the monotone line ...
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This paper deals with a new variant of the inexact restoration method of Fischer and Friedlander (Comput Optim Appl 46:333-346, 2010) for nonlinear programming. We propose an algorithm that replaces the monotone line search performed in the tangent phase by a non-monotone one, using the sharp Lagrangian as merit function. Convergence to feasible points satisfying the convex approximate gradient projection condition is proved under mild assumptions. Numerical results on representative test problems show that the proposed approach outperforms the monotone version when a suitable non-monotone parameter is chosen and is also competitive against other globalization strategies for inexact restoration.
This article considers the problem of designing a continuous-time dynamical system that solves a constrained nonlinear optimization problem and makes the feasible set forward invariant and asymptotically stable. The i...
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This article considers the problem of designing a continuous-time dynamical system that solves a constrained nonlinear optimization problem and makes the feasible set forward invariant and asymptotically stable. The invariance of the feasible set makes the dynamics anytime, when viewed as an algorithm, meaning it returns a feasible solution regardless of when it is terminated. Our approach augments the gradient flow of the objective function with inputs defined by the constraint functions, treats the feasible set as a safe set, and synthesizes a safe feedback controller using techniques from the theory of control barrier functions. The resulting closed-loop system, termed safe gradient flow, can be viewed as a primal-dual flow, where the state corresponds to the primal variables and the inputs correspond to the dual ones. We provide a detailed suite of conditions based on constraint qualification under which (both isolated and nonisolated) local minimizers are asymptotically stable with respect to the feasible set and the whole state space. Comparisons with other continuous-time methods for optimization in a simple example illustrate the advantages of the safe gradient flow.
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