High-Order Optimization Methods for Fully Composite Problems
本文统一研究了一类完全复合的凸优化问题，包括带函数约束、极大值最小化等类型，提出了新的高阶（p≥2）优化方法，并在一般条件下证明了全局收敛率。
In this paper, we study a fully composite formulation of convex optimization problems, which includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems with simple nondifferentiable components. We treat all these formulations in a unified way, highlighting the existence of very natural optimization schemes of different order $p \geq 1$. As the result, we obtain new high-order $(p \geq 2)$ optimization methods for composite formulation. We prove the global convergence rates for them under the most general conditions. Assuming that the upper-level component of our objective function is subhomogeneous, we develop efficient modification of the basic fully composite first-order and second-order methods and propose their accelerated variants.