Available online at: https://doi.org/10.1007/s10957-005-7497-6
Fan, Yueyue and Robert E. Kalaba (2005) A General Linear-Quadratic Optimization Problem. Journal of Optimization Theory and Applications 127 (3), 485 - 496
A linear-quadratic optimization problem is formulated in a dynamic programming manner. An updating formula for obtaining the solutions to such a problem is provided and illustrated using a few simple examples. This updating formula is also compared to a well-known updating formula for obtaining the inverses of symmetric positive-definite matrices. Numerical results are given.
Key Words: Dynamic programming, optimization, optimal production problems, linear-quadratic problems.