In this paper, we present a framework for modeling color liquid crystal displays (LCDs) having local light-emitting diode (LED) backlight with dimming capability. The proposed framework includes critical aspects like leakage, clipping, light diffusion and human perception of luminance and allows adjustable penalization of power consumption. Based on the framework, we have designed a set of optimization-based backlight dimming algorithms providing a perceptual optimal balance of clipping and leakage, if necessary. The novel algorithms are compared with several other schemes known from the literature, using both objective measures and subjective assessment. The results show that the novel algorithms provide better quality at a given energy level or lower energy at a given quality level.Index Terms-Backlight dimming, color image, contrast, high dynamic range (HDR), image quality, light-emitting diode (LED) backlight, light leakage, liquid crystal display (LCD), optimization, power saving.