Sentence examples for mathematical programming includes from inspiring English sources

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Mathematical programming includes the study of the mathematical structure of optimization problems, the invention of methods for solving these problems, the study of the mathematical properties of these methods, and the implementation of these methods on computers.

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Convexity plays a vital role in many aspects of mathematical programming including, for example, sufficient optimality conditions and duality theorems.

Convexity plays a central role in many aspects of mathematical programming including the analysis of stability, sufficient optimality conditions and duality.

It is known that (1.8) provides a convenient framework for the unified study of optimal solutions in many optimization related areas including mathematical programming, complementarity, variational inequalities, optimal control, mathematical economics, equilibria, game theory.

It is known that problem (1.9) provides a convenient framework for the unified study of optimal solutions in many optimization related areas including mathematical programming, complementarity problems, variational inequalities, optimal control, mathematical economics, equilibria, game theory, etc.

It is well known that problem (1.3) provides a convenient framework for the unified study of optimal solutions in many optimization related areas including mathematical programming, complementarity problems, variational inequalities, optimal control, mathematical economics, equilibria, and game theory, etc.

It is known that problem (1.7) provides a convenient framework for the unified study of optimal solutions in many optimization-related areas including mathematical programming, complementarity problems, variational inequalities, optimal control, mathematical economics, equilibria and game theory, etc.

It is known that problem (1.5) provides a convenient framework for the unified study of optimal solutions in many optimization related areas including mathematical programming, complementarity problems, variational inequalities, optimal control, mathematical economics, equilibria and game theory, etc.

It is known that (1.6) provides a convenient framework for the unified study of optimal solutions in many optimization related areas including mathematical programming, complementarity, variational inequalities, optimal control, mathematical economics, equilibria, and game theory.

It is known that (1.3) provides a convenient framework for the unified study of optimal solutions in many optimization-related areas including mathematical programming, complementarity, variational inequalities, optimal control, mathematical economics, equilibria, and game theory.

Several mathematical frameworks, including mathematical programming, have been proposed to incorporate equity considerations into resource allocation in the public sector [ 25- 29].

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