Kantorovich's Relaxation is an approach to solving linear programming problems by transforming them into more manageable forms, specifically through the relaxation of constraints to allow for fractional solutions. This method is particularly useful in the field of optimal transport and has significant applications in economics, logistics, and resource allocation problems.

Kantorovich's Relaxation

Linear programming problems

Relaxation of constraints

Fractional solutions are mathematical calculations where solutions to equations or optimization problems are allowed to be fractions or decimals, rather than just integers. This approach is often used in linear programming and combinatorial optimization to simplify problems and find approximate solutions more efficiently.

Fractional Solutions

Optimal Transport is a mathematical theory that studies the most efficient ways to move and transform distributions of mass, originally formulated by Monge and later expanded by Kantorovich. It has applications in various fields such as economics, machine learning, and fluid dynamics, providing a framework for comparing probability measures and solving resource allocation problems.

Optimal Transport

Economics is the study of how individuals, businesses, and governments make choices on allocating resources to satisfy their wants and needs, and how these choices interact to shape markets and economies. It encompasses both microeconomic and macroeconomic perspectives, analyzing everything from individual consumer behavior to global economic trends.

Economics

Logistics is the coordinated planning and execution of the movement and storage of goods, services, and information within a supply chain from origin to consumption. It plays a crucial role in ensuring efficiency, reducing costs, and enhancing customer satisfaction through effective resource management and strategic decision-making.

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