Approximate bregman proximal gradient algorithm for relatively smooth nonconvex optimization
提出近似Bregman近端梯度算法(ABPG)求解复合非凸优化问题，子问题更简单且常可闭式求解，在光滑部分梯度非全局Lipschitz时仍有效，数值实验表明优于现有算法。
Abstract In this paper, we propose the approximate Bregman proximal gradient algorithm (ABPG) for solving composite nonconvex optimization problems. ABPG employs a new distance that approximates the Bregman distance, making the subproblem of ABPG simpler to solve compared to existing Bregman-type algorithms. The subproblem of ABPG is often expressed in a closed form. Similarly to existing Bregman-type algorithms, ABPG does not require the global Lipschitz continuity for the gradient of the smooth part. Instead, assuming the smooth adaptable property, we establish the global subsequential convergence under standard assumptions. Additionally, assuming that the Kurdyka–Łojasiewicz property holds, we prove the global convergence for a special case. Our numerical experiments on the $$\ell _p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:math> regularized least squares problem, the $$\ell _p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:math> loss problem, and the nonnegative linear system show that ABPG outperforms existing algorithms especially when the gradient of the smooth part is not globally Lipschitz or even locally Lipschitz continuous.