نوع مقاله : مقاله پژوهشی
نویسندگان
1 بخش ریاضی کاربردی، دانشکده ریاضی و کامپیوتر، دانشگاه شهید باهنر کرمان، کرمان، ایران
2 گروه ریاضی، دانشکده علوم و فناوری‌های نوین، دانشگاه تحصیلات تکمیلی صنعتی و فناوری پیشرفته، کرمان، ایران
چکیده
کلیدواژه‌ها
موضوعات
عنوان مقاله [English]
نویسندگان [English]
The branch and bound algorithm is a widespread method for global optimization. This algorithm partitions the feasible set of the optimization problem through a branching method and then calculates an upper bound and a lower bound for each member of the partition using a bounding method. Finally, the branch and bound method compares the obtained bounds and the objective function values with each other and removes the members of the partition that do not contain an optimal point. In this paper, the branch and bound algorithm for optimizing increasing co-radiant functions on subsets of $\mathbb{R}_+^n$ which are presented in the form of the intersection of a half-space with a simplex (the purpose of considering such feasible sets is to examine a model of financial mathematics, called the mean-standard deviation model). We use the concept of abstract convexity to increase co-radiant functions for bounding (finding lower bounds). In the end, as an application of this optimization problem, we propose the mean-standard deviation model of portfolio optimization and solve it with the branch and bound method.
کلیدواژه‌ها [English]
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