Novel optimization techniques for inferring heterogeneous population dynamics

Area of Science:

• Computational Biology
• Optimization Algorithms
• Mathematical Modeling

Background:

• Parameter estimation for heterogeneous population dynamics presents significant computational challenges.
• Existing optimization methods struggle with the complex inequality and equality constraints common in these problems.
• Non-convex objective functions in parameter estimation often lead to multiple critical points, hindering global minimum identification.

Purpose of the Study:

• Introduce a novel optimization algorithm, cubic regularized Newton with affine scaling (CRNAS), designed for parameter estimation in heterogeneous population dynamics.
• Address the limitations of first-order methods by incorporating second-order optimality conditions.
• Develop a robust method for handling both inequality (box) and equality constraints.

Main Methods:

• CRNAS utilizes the Hessian of the objective function, enabling convergence to points satisfying second-order optimality conditions.
• An affine scaling approach is employed to effectively manage a broad range of constraints, including equality constraints.
• Theoretical analysis demonstrates CRNAS converges to $ \epsilon $-approximate second-order optimality within $ O(\epsilon^{-3/2}) $ iterations.

Main Results:

• CRNAS demonstrates strong performance in parameter estimation for heterogeneous population models.
• Numerical simulations show CRNAS is comparable or superior to MATLAB's fmincon in accuracy and computational cost.
• The algorithm effectively handles the mixed population dynamics characteristic of the test problems.

Conclusions:

• CRNAS is a powerful and efficient optimization algorithm for parameter estimation in heterogeneous population dynamics.
• The method's ability to handle complex constraints and non-convex objectives makes it suitable for challenging biological modeling tasks.
• CRNAS offers a competitive alternative to existing solvers for problems involving mixtures of populations.