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<p>In this work, a new sufficient condition for the existence of a unique root of a continuously differentiable real-valued function of one variable is presented. Conditions are also given under which one can conclude that the function has no root. Specific applications in financial planning and operations management are shown to satisfy these sufficient conditions. These results also have implications for the line-search problem, which is used in most algorithms for solving differentiable nonlinear optimization problems.</p>

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Sufficient Conditions for a Real-Valued Function to have a Unique Root or No Root at All

  • 期刊论文

  • 发表日期：

    2025年1月8日

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  • Daniel Solow,
  • Qi Wu

摘要

In this work, a new sufficient condition for the existence of a unique root of a continuously differentiable real-valued function of one variable is presented. Conditions are also given under which one can conclude that the function has no root. Specific applications in financial planning and operations management are shown to satisfy these sufficient conditions. These results also have implications for the line-search problem, which is used in most algorithms for solving differentiable nonlinear optimization problems.