Let ${{B}_{p}}$ be the unit ball in ${{\mathbb{L}}_{p}}$ , $0\,<\,p\,<\,1$, and let $\Delta _{+}^{s}$ , $s\,\in \,\mathbb{N}$, be the set of all $s$-monotone functions on a finite interval $I$, i.e., $\Delta _{+}^{s}$ consists of all functions $x\,:\,I\,\mapsto \,\mathbb{R}$ such that the divided differences $[x;\,{{t}_{0}},\,...\,,\,{{t}_{s}}]$ of order $s$ are nonnegative for all choices of $\left( s\,+\,1 \right)$ distinct points ${{t}_{0}},\,.\,.\,.\,,{{t}_{s}}\,\in \,I.$ For the classes $\Delta _{+}^{s}{{B}_{P}}\,:=\,\Delta _{+}^{s}\,\cap \,{{B}_{P}},$ we obtain exact orders of Kolmogorov, linear and pseudo-dimensional widths in the spaces ${{\mathbb{L}}_{q}},$$0\,<\,q\,<\,p\,<\,1$:

$${{d}_{n}}(\Delta _{+}^{s}{{B}_{P}})_{{{\mathbb{L}}_{q}}}^{\text{psd}}\asymp {{d}_{n}}(\Delta _{+}^{s}{{B}_{P}})_{{{\mathbb{L}}_{q}}}^{\text{kol}}\asymp {{d}_{n}}(\Delta _{+}^{s}{{B}_{P}})_{{{\mathbb{L}}_{q}}}^{\text{lin}}\asymp {{n}^{-s}}.$$