Abstract
This paper presents a simple and direct proof of the dual optimization problem. The stationary conditions of the original and the dual problems are exactly equivalent, and the duality gap can be completely eliminated in the dual problem, where the maximal or minimal value is solved together with the stationary conditions of the dual problem and the original constraints. As an illustration, optimization of SiC/graphene composite is addressed with an objective of maximizing certain material properties under the constraint of a given strength.
Highlights
IntroductionOptimization is an important branch of mathematics that aims at finding the optimal solution (maximum or minimum) of a given problem and under given constraints
Optimization is an important branch of mathematics that aims at finding the optimal solution of a given problem and under given constraints
In this short letter we give a direct proof of the dual optimization problem without using the Lagrange multiplier theory
Summary
Optimization is an important branch of mathematics that aims at finding the optimal solution (maximum or minimum) of a given problem and under given constraints. It is sufficient to optimize individual components of the system and assemble the entire system This is obviously a simplified approach compared to considering the system as a whole, but it produces satisfactory results on many occasions. Depending on the type of problem to be resolved, the same approach can be successfully applied in other disciplines, including mechanical engineering. In this short letter we give a direct proof of the dual optimization problem without using the Lagrange multiplier theory
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