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Convergence of exponential penalty function method for Variational Problems

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES 2019年第3期89卷 517-524页

作者： Jayswal, Anurag Choudhury, Sarita Indian Sch Mines Dept Appl Math Dhanbad 826004 Jharkhand India Sci Coll Autonomous Dept Math Ganjam 761102 Odisha India

In this paper, we propose an exponential penalty function method in order to solve a constrained variational problem by transforming it into a sequence of unconstrained ones. Further, we analyze the relationship between the optimal solutions of the sequence of exponential penalized variational problems and that of the original constrained variational problem. The convergence of this exponential penalty method is also examined for variational problems. Numerical examples are provided to verify the obtained results and validate the efficient use of exponential penalty method for solving constrained variational problems.

关键词： exponential penalty function method Variational problem Convergence

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The exponential penalty function method for multiobjective programming problems

The exponential penalty function method for multiobjective p...

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2nd International Conference on Nonlinear Programming with Applications

作者： Liu, Sanming Feng, Enmin Shanghai Dianji Univ Dept Math & Phys Shanghai 200240 Peoples R China Dalian Univ Technol Dept Appl Math Dalian Peoples R China

Following the classical exponential penalty function method of mathematical programming, the exponential penalty function method of multiobjective programming problems (MOPP) is constructed and its convergence is prov... 详细信息

关键词： multiobjective programming exponential penalty function method convergence

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The exponential penalty function method for multiobjective programming problems

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OPTIMIZATION methodS & SOFTWARE 2010年第5期25卷 667-675页

作者： Liu, Sanming Feng, Enmin Shanghai Dianji Univ Dept Math & Phys Shanghai 200240 Peoples R China Dalian Univ Technol Dept Appl Math Dalian Peoples R China

关键词： multiobjective programming exponential penalty function method convergence

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On convergence of exponential penalty for the multi-dimensional variational problems

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RAIRO-OPERATIONS RESEARCH 2023年第2期57卷 927-938页

作者： Jayswal, Anurag Baranwal, Ayushi Indian Inst Technol Indian Sch Mines Dept Math & Comp Dhanbad 826004 India

In this article, we describe a method to deal with a multi-dimensional variational problem with inequality constraints using an exponential penalty function. We formulate an unconstrained multi-dimensional variational problem and examine the relationships between the optimal solution to the considered multi-dimensional variational problem and the sequence of minimizers of the unconstrained multi-dimensional variational problem. The convergence of the proposed exponential penalty approach is also investigated, which shows that a convergent subsequence of the sequence of minimizers of the unconstrained multi-dimensional variational problem approaches an optimal solution to the multi-dimensional variational problem. Further, an illustrative application (to minimize a manufacturing cost functional of a production firm) is also presented to confirm the effectiveness of the proposed outcomes.

关键词： Convergence exponential penalty function method optimal solution multi-dimensional variational problem

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