Imoukhedeme Paul Kehinde is a mathematician and financial engineering specialist with strong expertise in mathematical modelling, stochastic processes, and machine learning. He holds an M.Sc. in Mathematics (First Class, CGPA 4.92/5.00) from Usmanu Danfodiyo University, Sokoto, Nigeria, and an M.Sc. in Financial Engineering (Distinction) from WorldQuant University, USA. His academic background combines rigorous theoretical foundations with advanced computational applications. His research interests include discrete mathematics, probabilistic combinatorics, spectral graph theory, stochastic modelling, and optimization techniques, with applications in epidemiology, healthcare systems, and quantitative finance. He has published peer-reviewed research on fractional-order grey models for tax revenue forecasting, malaria and Lyme disease modelling, and MCMC estimation of Heston stochastic volatility models for option pricing. Paul has presented at national conferences, including the Annual Conference of the Nigerian Mathematical Society. He currently serves as a Research Analyst and Mathematics Instructor, contributing to applied mathematics, econometric modelling, and policy-focused quantitative research. His work reflects a strong commitment to leveraging mathematical innovation to address complex real-world challenges.

A DERIVATIVE-FREE OPTIMIZATION METHOD ON HADAMARD MANIFOLD FOR SOLVING NONLINEAR MONOTONE SYSTEMS WITH APPLICATION IN IMAGE DEBLURRING:This work develops an innovative derivative-free optimization method which is a con vex combination of two well-known methods, Fletcher–Reeves and Polak-Ribi`ere-Polyak, for solving large-scale nonlinear monotone system on Hadamard manifolds. Most convectional Riemannian optimization methods require gradients or the Jacobian matrix, which may be computationally expensive or unavailable, especially on curved spaces. This approach inte grates hybrid conjugate gradient strategies with hypersurface projection techniques adapted via retractions and vector transport to guarantee solution on the manifold. An important feature of the Algorithm is its use of function-based line search rules, incorporating Armijo and Wolfe-type conditions, which ensure sufficient descent without relying on derivative of the operator while it combats the issues of stagnation. The convergence analysis confirms global convergence of iterates under monotonicity and Lipschitz continuity assumptions. Further more, the study perform numerical experiments on problems with dimensions up to 50,000 which demonstrate the method’s efficiency, stability, and competitiveness compared to ex isting methods and finally, when applied to image restoration, it successfully reconstructs corrupted images with high image quality, as measured by standard metrics such as Peak Signal-to-Noise Ratio (PSNR) and Signal-to-Noise Ratio (SNR).