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Ludwig (Lev) Kantorovich (1912–1986)

Founder of Linear Programming and Resource Optimization

Ludwig Borisovich Kantorovich, a Soviet mathematician and economist, pioneered linear programming and optimization. His 1939 breakthrough recast the problem of allocating resources efficiently as a linear optimization problem:

• Maximize \( z = \mathbf{c}^T \mathbf{x} \) subject to \( A \mathbf{x} \leq \mathbf{b}, \mathbf{x} \ge 0\).

He developed duality theory and economic interpretations for these mathematical constructs, showing how price vectors can represent shadow prices of resources.

Contributions

• Duality theory: introduced complementary slackness between primal and dual problems.
• Approximate methods: utilized functional analysis and mixed-integer methods in economic planning.
• Computational applications: applied his methods to optimize timber and industrial production planning in Siberia.

Legacy

Kantorovich received the Nobel Memorial Prize in Economic Sciences in 1975 for his contributions to resource allocation theory. His work established mathematical economics and optimization as fields, influencing operations research worldwide.