Use case
Robust Solutions to the Life-Cycle Consumption Problem
The life-cycle consumption problem consists in determining the best consumption pattern and investment decisions of individuals over their lifetime. Confronted with a high degree of uncertainty and the need to incorporate budgetary constraints, the results obtained include instances with a 30-year time horizon and improved outcomes, particularly in the most unfavorable scenarios.

The objective of this research is the maximization of the utility function subject to lifetime budget constraints such as personal income and consumption in each period, investments in assets, need to save for retirement, characterized by different interest rates, and discount factors. For instance, an individual may want to maximize the utility obtained by spending money on food, rent, sports, hobbies, and investments with a given monthly salary.

Due to the uncertain nature of future income and investment returns, a robust optimization approach is used to deal with the life-cycle consumption problem to find solutions that perform well even in adverse conditions. However, this problem can be hard to solve when long horizons and different assumptions related to the degree of uncertainty of the future are considered.

Thanks to Artelys Knitro and the methodology proposed by the authors, instances with a time horizon of 30 years can be solved efficiently, and solutions that deliver the highest utility for worst-case scenarios of future returns can be identified.

Start with a tutorial!


You’re not familiar with nonlinear optimization? This tutorial will present some examples of nonlinear problems for various applications. You will discover nonlinear programming methods using the Artelys Knitro solver in a Python notebook, through different examples.

Free trial


Get your trial license to test Artelys Knitro’s performances on your own mathematical optimization problem. The trial package includes free support and maintenance. You can have access to Artelys Knitro for free with a 1-month unlimited version or a 6-month limited version.

Artelys Knitro has unmatched performance

Best Nonlinear Solver

Artelys Knitro has been ranked every year by public benchmarks consistently showing Artelys Knitro finds both feasible and proven optimal solutions faster than competing solvers.

Technical support

The Artelys technical support team comprises Artelys’consultants (PhD-level) who are used to solving the most difficult problems and deploying enterprise-wide optimization solutions. They can advise on algorithmic or software features that may result in enhanced performance in your usage of Artelys Knitro.

Updates and new features

The development team works continuously to provide two releases of Artelys Knitro every year. Based on feedback, we always improve our solver to meet users’ requirements and need to solve larger models faster.

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