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Lower semicontinuity of approximate solution mappings for parametric generalized vector equilibrium problems

JOURNAL OF INEQUALITIES AND APPLICATIONS 2014年第1期2014卷 1-9页

作者： Wangkeeree, Rabian Boonman, Panatda Preechasilp, Pakkapon Naresuan Univ Dept Math Fac Sci Phitsanulok 65000 Thailand Pibulsongkram Rajabhat Univ Program Math Fac Educ Phitsanulok 65000 Thailand

In this paper, we obtain sufficient conditions for the lower semicontinuity of an approximate solution mapping for a parametric generalized vector equilibrium problem involving set-valued mappings. By using a scalarization method, we obtain the lower semicontinuity of an approximate solution mapping for such a problem without the assumptions of monotonicity and compactness.

关键词： lower semicontinuity approximate solution mapping parametric generalized vector equilibrium problems scalarization method

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Obtaining Optimal Pareto Front Approximations using Scalarized Preference Information 15

Obtaining Optimal Pareto Front Approximations using Scalariz...

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17th Genetic and Evolutionary Computation Conference (GECCO)

作者： Braun, Marlon Shukla, Pradyumn Kumar Schmeck, Hartmut KIT Inst AIFB Dortmund Germany Tech Univ Clausthal Inst Math Dortmund Germany

ISBN: (纸本)9781450334723

scalarization techniques are a popular method for articulating preferences in solving multi-objective optimization problems. These techniques, however, have so far proven to be ill-suited in finding a preference-driven approximation that still captures the Pareto front in its entirety. Therefore, we propose a new concept that defines an optimal distribution of points on the front given a specific scalarization function. It is proven that such an approximation exists for every real-valued problem irrespective of the shape of the corresponding front under some very mild conditions. We also show that our approach works well in obtaining an equidistant approximation of the Pareto front if no specific preference is articulated. Our analysis is complemented by the presentation of a new algorithm that implements the aforementioned concept. We provide in-depth simulation results to demonstrate the performance of our algorithm. The analysis also reveals that our algorithm is able to outperform current state-of-the-art algorithms on many popular benchmark problems.

关键词： multi-objective optimization scalarization method preference-based approximation electromagnetism-like mechanism

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Power-Throughput Tradeoff in MIMO Heterogeneous Networks

Power-Throughput Tradeoff in MIMO Heterogeneous Networks

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47th Asilomar Conference on Signals, Systems and Computers

作者： Manosha, K. B. Shashika Joshi, S. Codreanu, M. Rajatheva, N. Latva-aho, M. Univ Oulu Ctr Wireless Commun FIN-90014 Oulu Finland

ISBN: (纸本)9781479923908

We consider a single-macrocell heterogeneous multiple-input multiple-output network, where the macrocell shares the same frequency band with the femto network. The interference power to the macro users from the femto base stations is kept below a threshold to guarantee that the performance of the macro users does not degrade due to femto network. For this setting, we consider the problem of finding the set of all achievable power-rate tuples. Using the scalarization method, we cast the problem of finding the set of achievable power-rate tuples as a mathematical optimization problem. Using simulations we obtained the different sets of all achievable power-rate values, when the users are served by both macrocell and femtocells, and only by macrocell.

关键词： achievable power-rate values scalarization method heterogeneous networks multi-input multi-output (MIMO)

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Adaptive Weighted Aggregation: A Multiobjective Function Optimization Framework Taking Account of Spread and Evenness of Approximate Solutions

Adaptive Weighted Aggregation: A Multiobjective Function Opt...

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2010 IEEE World Congress on Computational Intelligence

作者： Hamada, Naoki Nagata, Yuichi Kobayashi, Shigenobu Ono, Isao Tokyo Inst Technol Interdisciplinary Grad Sch Sci & Engn Yokohama Kanagawa 2268502 Japan

ISBN: (纸本)9781424481262

The multi-starting descent method is a promising approach to unimodal multiobjective function optimization problems because of its precision of obtained solutions. Descent methods can be classified into two categories;the multiobjective descent method directly using the Jacobian matrix of objective functions and the scalarized descent method using the gradient of a scalarized objective function. In the multiobjective descent method and the scalarized descent method, a convergent point depends on an initial solution and a weight vector, respectively. However, it is difficult to choose appropriate initial solutions or weight vectors for obtaining widely and evenly distributed solutions. In order to remedy the problems of the conventional methods, we propose a multi-starting scalarized descent method named AWA that employs the Chebyshev norm method as a scalarization method and an adaptive scheme of weight vectors for the scalarization method. We show the effectiveness of the proposed method through some experiments.

关键词： AWA Chebyshev norm method Jacobian matrices Jacobian matrix adaptive weighted aggregation approximate solutions multiobjective function optimization framework multistarting descent method multistarting scalarized descent method objective functions optimisation scalarization method unimodal multiobjective function optimization problems weight vectors

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Fixed point theorems for set-valued contractions

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RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO 2013年第3期62卷 367-377页

作者： Amini-Harandi, A. Fakhar, M. Hajisharifi, H. R. Univ Shahrekord Dept Pure Math Shahrekord 88186 Iran Inst Res Fundamental Sci IPM Sch Math Tehran Iran Univ Isfahan Dept Math Esfahan 81745163 Iran

In this paper, we obtain some fixed point theorems for new set-valued contractions in complete metric spaces. Then by using these results and the scalarization method, we present some fixed point theorems for set-valued contractions in complete cone metric spaces without the normality assumption. We also present some examples to support our results.

关键词： Fixed point Cone metric space Ordered Banach space scalarization method

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OPTIMAL STOPPING PROBLEM WITH A VECTOR-VALUED REWARD FUNCTION

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2014年第6期35卷 777-781页

作者： Makasu, Cloud Univ Western Cape Dept Math & Appl Math ZA-7535 Bellville South Africa

In this note, using the well-known method of scalarization, we give an explicit characterization of the Pareto optimal stopping time for a vector-valued optimal stopping problem with only two reward functions. The pre... 详细信息

关键词： Geometric Brownian motions scalarization method Vector-valued optimal stopping problem 58E17 60G40 62L15

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A Generalization of the Concept of Proper Efficiency in the Decomposed Multi-Objective Optimization Problems

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2024年第13-14期45卷 686-704页

作者： Foroutannia, Davoud Ahmadi, Fatemeh Vali e Asr Univ Rafsanjan Dept Math Rafsanjan Iran

In the context of multi-objective optimization, a properly efficient solution is one that is efficient while at least one of the tradeoffs between different objectives is limited. However, in some situations, it is possible that all efficient solutions have unlimited tradeoffs, which is not always appropriate. To provide new solutions that have at least one bounded tradeoff for such problems, we first introduce a new concept of efficiency by applying a family of scalarization functions for the decomposed multi-objective optimization problem. Then, we extend the concept of proper efficiency by examining the boundedness of the tradeoffs between scalar optimization subproblems and other subproblems. Another purpose of this paper is to investigate the effect of using the scalarizing functions for some subproblems in the decomposed multi-objective optimization problem. Our findings suggest that as the number of subproblems that use scalarizing functions increases, the solution set associated with the generalized proper efficiency concept becomes smaller.

关键词： Efficiency multi-objective optimization proper efficiency proper efficiency with respect to a partition scalarization method

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A set-valued generalization of Ricceri's theorem related to Fan-Takahashi minimax inequality

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Nihonkai Mathematical Journal 2015年第2期26卷 135-144页

作者： Yutaka Saito Tamaki Tanaka

In the paper, we propose Ricceri type theorem on Fan-Takahashi minimax inequality for set-valued maps by using the scalarization method proposed by Kuwano, Tanaka and Yamada based on a certain type of the set-relations.

关键词： 49J53 ‎54C60‎ 90C29 Fan-Takahashi minimax inequality Ricceri's theorem scalarization method set-relations set-valued map

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Lagrangian Relaxation method for Multiobjective Optimization methods: Solution Approaches

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Journal of Applied Mathematics and Physics 2022年第5期10卷 1619-1630页

作者： H. S. Faruque Alam Department of Mathematics University of Chittagong Chittagong Bangladesh

This paper introduces the Lagrangian relaxation method to solve multiobjective optimization problems. It is often required to use the appropriate technique to determine the Lagrangian multipliers in the relaxation method that leads to finding the optimal solution to the problem. Our analysis aims to find a suitable technique to generate Lagrangian multipliers, and later these multipliers are used in the relaxation method to solve Multiobjective optimization problems. We propose a search-based technique to generate Lagrange multipliers. In our paper, we choose a suitable and well-known scalarization method that transforms the original multiobjective into a scalar objective optimization problem. Later, we solve this scalar objective problem using Lagrangian relaxation techniques. We use Brute force techniques to sort optimum solutions. Finally, we analyze the results, and efficient methods are recommended.

关键词： Multiobjective Optimization Problem Lagrangian Relaxation Lagrange Multipliers scalarization method

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Lipschitz continuity of an approximate solution mapping for parametric set-valued vector equilibrium problems

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OPTIMIZATION 2016年第5期65卷 1003-1021页

作者： Sadeqi, I. Paydar, M. Salehi Sahand Univ Technol Dept Math Tabriz Iran

The purpose of this paper is to generalize and improve some topological properties of solutions set to the set-valued vector equilibrium problems by using the scalar characterization method. Moreover, the Lipschitz co... 详细信息

关键词： set-valued vector equilibrium problem approximate solution mapping scalarization method Lipschitz continuity 49J40 49K40 90C31

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