To determine which term is an exception to the principle of optimum use of health investment, we need to consider each option in terms of how it relates to efficiently allocating resources to improve health outcomes.

1. Administrative streamlining: This involves improving the efficiency of administrative processes, thereby reducing unnecessary bureaucracy and improving resource allocation. By reducing waste in administrative tasks, more resources can be directed towards patient care, making it an effective part of health investment strategies.
2. Supplier induced demand: This occurs when healthcare providers influence a patient's decision, leading to potentially unnecessary services or treatments. While it may increase demand and potential revenue, it does not align with the efficient or optimal use of health investment as it can lead to overutilization of services.
3. Geographic urgency: This refers to prioritizing health resources in areas with urgent needs, such as outbreaks or locations with severe healthcare deficiencies. It ensures that health investments are directed where they are most needed, aligning with efficient use of resources.
4. Catastrophic health expenditure: This term refers to health expenses that threaten a household's financial stability, resulting from high out-of-pocket costs. While this is a critical issue in health financing, it is a consequence of inefficient health spending, rather than a principle for optimizing investment. Thus, it does not align with the concept of optimal use of health investment.

Conclusion: The term Catastrophic health expenditure is the exception to optimizing health investment as it reflects financial vulnerability and inefficiency rather than a strategy for effective resource use.