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Optimization means a process of searching for the best solution under given conditions. From the viewpoint of this introductory book, it is considered a mathematical discipline that searches for an extremumExtremum (i.e., a minimumMinimum or a maximum)Maximum \({\mathbf{x}}^{*}\) of a given objective functionFunctionobjective \(f\left( {\mathbf{x}} \right)\) defined on a particular set. Hence, the extremumPointextremum result has usually the form of a pointPoint or a vectorVector over real numbers. This kind of optimization is also called parameter optimization, static optimization, or operations research. It is worth noting that this book does not intend to present more advanced problems of the calculus of variations, in which the goal is to find an optimal function \(f^{*} \left( {\mathbf{x}} \right)\) that extremizes a certain functional \(\Phi \left( {f\left( {\mathbf{x}} \right)} \right)\) under specific conditions. The following two simple examples elucidate the difference.

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Introduction

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  • 发表日期：

    2025年

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  • Libor Pekař

摘要

Optimization means a process of searching for the best solution under given conditions. From the viewpoint of this introductory book, it is considered a mathematical discipline that searches for an extremumExtremum (i.e., a minimumMinimum or a maximum)Maximum \({\mathbf{x}}^{*}\) of a given objective functionFunctionobjective \(f\left( {\mathbf{x}} \right)\) defined on a particular set. Hence, the extremumPointextremum result has usually the form of a pointPoint or a vectorVector over real numbers. This kind of optimization is also called parameter optimization, static optimization, or operations research. It is worth noting that this book does not intend to present more advanced problems of the calculus of variations, in which the goal is to find an optimal function \(f^{*} \left( {\mathbf{x}} \right)\) that extremizes a certain functional \(\Phi \left( {f\left( {\mathbf{x}} \right)} \right)\) under specific conditions. The following two simple examples elucidate the difference.