Video coding that pursues the highest compression efficiency is the art of computing for rate-distortion optimization. The optimization has been approached in different ways, exemplified by two typical frameworks: block-based hybrid video coding and end-to-end learned video coding. The block-based hybrid framework encompasses more and more coding modes that are available at the decoder side; an encoder tries to search for the optimal coding mode for each block to be coded. This is an online, discrete, search-based optimization strategy. The end-to-end learned framework embraces more and more sophisticated neural networks; the network parameters are learned from a collection of videos, typically using gradient descent-based methods. This is an offline, continuous, numerical optimization strategy. Having analyzed these two strategies, both conceptually and with concrete schemes, this paper suggests investigating hybrid -optimization video coding, that is to combine online and offline, discrete and continuous, search-based and numerical optimization. For instance, we propose a hybrid-optimization video coding scheme, where the decoder consists of trained neural networks and supports several coding modes, and the encoder adopts both numerical and search-based algorithms for the online optimization. Our scheme achieves promising compression efficiency on par with H.265/HM for the random-access configuration.