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lipschitz programming via increasing convex-along-rays functions

OPTIMIZATION METHODS & SOFTWARE 1999年第6期10卷 763-781页

作者： Rubinov, A Andramonov, V Univ Ballarat Sch Informat Technol & Math Sci Ballarat Vic 3353 Australia

We propose a general scheme of reduction of a lipschitz programming problem to a problem of minimizing increasing convex-along-rays function. It is based on the positively homogeneous extension of degree p of the objective function and projective transformation of R-+(n) onto the unit simplex. The application of cutting angle method to lipschitz programming is considered.

关键词： lipschitz programming abstract convexity cutting angle method

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ERROR-BOUNDS FOR GENERALIZED LAGRANGE MULTIPLIERS IN LOCALLY lipschitz programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1992年第1期73卷 205-210页

作者： PAPPALARDO, M 1. Department of Mathematics University of Pisa Pisa Italy

Recent studies are concerned with two types of questions in nonconvex optimization: (a) conditions for having bounded Lagrange multipliers, Refs. 1-2;(b) a priori bounds for such Lagrange multipliers, Ref. 3. Such topics have been investigated under suitable regularity assumptions. The purpose of this paper is to study the same problems for the generalized Lagrange multipliers of a locally lipschitz programming.

关键词： GENERALIZED LAGRANGE MULTIPLIERS GENERALIZED DERIVATIVES lipschitz programming

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Scheduling of transportation fleet maintenance service by an improved lipschitz optimization algorithm

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OPTIMIZATION METHODS & SOFTWARE 2014年第3期29卷 592-609页

作者： Yao, Ming-Jong Huang, Jia-Yen Natl Chiao Tung Univ Dept Transportat & Logist Management Hsinchu 300 Taiwan Natl Chin Yi Univ Technol Dept Informat Management Taichung 41170 Taiwan

This study proposes a new and improved lipschitz optimization algorithm to obtain an E-optimal solution for solving the transportation fleet maintenance-scheduling problem. It employs a procedure based on slope-checking and step-size comparison mechanisms to improve the computational efficiency of the Evtushenko algorithm. Our numerical experiments used 36,000 randomly generated instances to compare the run time and solution quality of our proposed algorithm with the alternative approach in the literature. Our results indicate that the run time of the proposed algorithm could be significantly improved by more than 80% in over 50% of instances in our numerical experiments. We conclude that our proposed algorithm significantly improves the computational efficiency of the conventional Evtushenko algorithm.

关键词： lipschitz programming optimization Evtushenko algorithm maintenance scheduling

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Local optimization method with global multidimensional search

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JOURNAL OF GLOBAL OPTIMIZATION 2005年第2期32卷 161-179页

作者： Bagirov, AM Rubinov, AM Zhang, JP Univ Ballarat Sch Informat Technol & Math Sci Ctr Informat & Appl Optimizat Ballarat Vic 3353 Australia

This paper presents a new method for solving global optimization problems. We use a local technique based on the notion of discrete gradients for finding a cone of descent directions and then we use a global cutting angle algorithm for finding global minimum within the intersection of the cone and the feasible region. We present results of numerical experiments with well-known test problems and with the so-called cluster function. These results confirm that the proposed algorithms allows one to find a global minimizer or at least a deep local minimizer of a function with a huge amount of shallow local minima.

关键词： derivative-free optimization discrete gradient global optimization lipschitz programming the cutting angle method

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Solving DC programs using the cutting angle method

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JOURNAL OF GLOBAL OPTIMIZATION 2015年第1期61卷 71-89页

作者： Ferrer, Albert Bagirov, Adil Beliakov, Gleb Univ Politecn Cataluna Dept Matemat Aplicada I Barcelona Spain Univ Ballarat Sch Sci Informat Technol & Engn Ballarat Vic 3353 Australia Deakin Univ Sch Engn & Informat Technol Melbourne Vic Australia

In this paper, we propose a new algorithm for global minimization of functions represented as a difference of two convex functions. The proposed method is a derivative free method and it is designed by adapting the extended cutting angle method. We present preliminary results of numerical experiments using test problems with difference of convex objective functions and box-constraints. We also compare the proposed algorithm with a classical one that uses prismatical subdivisions.

关键词： DC programming lipschitz programming Cutting Angle method

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REFINEMENTS OF NECESSARY CONDITIONS FOR OPTIMALITY IN NONLINEAR-programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1992年第1期73卷 65-74页

作者： FACCHINEI, F 1. Dipartimento di Informatica e Sistemistica Università di Roma “La Sapienza” Roma Italy

In this paper, a new set of necessary conditions for optimality is introduced with reference to the differentiable nonlinear programming problem. It is shown that these necessary conditions are sharper than the usual Fritz John ones. A constraint qualification relevant to the new necessary conditions is defined and extensions to the locally lipschitz case are presented.

关键词： NONLINEAR programming lipschitz programming NECESSARY OPTIMALITY CONDITIONS CONSTRAINT QUALIFICATIONS

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A multidimensional descent method for global optimization

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OPTIMIZATION 2009年第5期58卷 611-625页

作者： Bagirov, Adil M. Rubinov, Alexander M. Zhang, Jiapu Univ Ballarat Ctr Informat & Appl Optimizat Sch Informat Technol & Math Sci Ballarat Vic 3353 Australia

This article presents a new multidimensional descent method for solving global optimization problems with box-constraints. This is a hybrid method where local search method is used for a local descent and global search is used for further multidimensional search on the subsets of intersection of cones generated by the local search method and the feasible region. The discrete gradient method is used for local search and the cutting angle method is used for global search. Two-and three-dimensional cones are used for the global search. Such an approach allows one, as a rule, to escape local minimizers which are not global ones. The proposed method is local optimization method with strong global search properties. We present results of numerical experiments using both smooth and non-smooth global optimization test problems. These results demonstrate that the proposed algorithm allows one to find a global or a near global minimizer.

关键词： global optimization discrete gradient derivative-free optimization the cutting angle method lipschitz programming

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Comparative analysis of the cutting angle and simulated annealing methods in global optimization

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OPTIMIZATION 2003年第4-5期52卷 363-378页

作者： Bagirov, AM Zhang, JP Univ Ballarat Ctr Informat & Appl Optimizat Sch Informat Technol & Math Sci Ballarat Vic 3353 Australia

This article presents a comparative analysis of two methods of global optimization: the simulated annealing method and a method based on a combination of the cutting angle method and a local search. This analysis is carried out using results of numerical experiments. These results demonstrate that the combined method is more effective than the simulated annealing method.

关键词： global optimization the simulated annealing method the cutting angle method lipschitz programming

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Cutting angle method and a local search

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JOURNAL OF GLOBAL OPTIMIZATION 2003年第2-3期27卷 193-213页

作者： Bagirov, AM Rubinov, AM Univ Ballarat Sch Informat Technol & Math Sci Ballarat Vic 3353 Australia

The paper deals with combinations of the cutting angle method in global optimization and a local search. We propose to use special transformed objective functions for each intermediate use of the cutting angle method. We report results of numerical experiments which demonstrate that the proposed approach is very beneficial in the search for a global minimum.

关键词： global optimization cutting angle method lipschitz programming discrete gradient

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Cutting angle method and a local search

Cutting angle method and a local search

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International Workshop on Optimization with High Technology Applications

作者： Bagirov, AM Rubinov, AM Univ Ballarat Sch Informat Technol & Math Sci Ballarat Vic 3353 Australia

关键词： global optimization cutting angle method lipschitz programming discrete gradient

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