primal-dual method (english) - meaning, definition, translation, pronunciation

Part of Speech

Noun Phrase

Phonetic Transcription

/prɪməl ˈdjuːəl ˈmɛθəd/

Meaning and Usage

The "primal-dual method" is an optimization technique commonly used in mathematical programming, particularly in linear programming and convex optimization. It simultaneously considers both the primal problem (which seeks to minimize a certain objective function) and its dual problem (which seeks to maximize a dual function related to the original constraints). This method aids in finding optimal solutions more efficiently than tackling each problem separately.

The term is more frequently used in written contexts, especially within academic papers, textbooks, and professional discussions related to optimization methods in mathematics, engineering, and computer science.

Example Sentences

1. The researcher applied the primal-dual method to enhance the efficiency of the algorithm.
2. Исследователь применил метод примал-дуал для повышения эффективности алгоритма.
3. By using the primal-dual method, we were able to solve the optimization problem in less time.
4. Используя метод примал-дуал, мы смогли решить задачу оптимизации за меньшее время.
5. The lecture on the primal-dual method illuminated its applications in network flow problems.
6. Лекция о методе примал-дуал прояснила его применение в задачах сетевого потока.

Idiomatic Expressions

While "primal-dual method" does not have widely recognized idiomatic expressions associated with it, in the context of optimization and mathematical programming, the terms "primal" and "dual" appear in discussions about problem-solving techniques. Here are some phrases that might pop up in discussions around this topic:

1. "Primal solution"
2. The primal solution provides a base for analyzing feasible regions.

3. Примальное решение дает основу для анализа допустимых областей.

4. "Dual variables"

5. The dual variables give insight into the sensitivity of the optimal solution.

6. Двойственные переменные дают представление о чувствительности оптимального решения.

7. "Optimality conditions"

8. Understanding the optimality conditions is crucial when applying the primal-dual method.
9. Понимание условий оптимальности имеет решающее значение при применении метода примал-дуал.

Etymology

The term "primal" derives from the Latin word "primalis," meaning "first" or "primary," while "dual" comes from the Latin "dualis," meaning "twofold." The use of "method" in this context indicates a systematic way of approaching the optimization problem. The combination reflects the dual nature of optimization problems in mathematical programming, focusing on two perspectives of the same issue.

Synonyms and Antonyms

Synonyms

• Duality approach
• Simultaneous optimization
• Primal-dual algorithm

Antonyms

• Primal method (without dual considerations)
• Isolated optimization
• Single solution approach