带等式和不等式约束的非光滑DC优化问题的精确罚DCA调控方法

改进的提升差分凸算法用于非光滑函数及其在图像恢复中的应用

An Improved Boosted DC Algorithm for Nonsmooth Functions with Applications in Image Recovery

改进的提升差分凸算法用于非光滑函数，通过单调线搜索提升收敛性，在图像恢复中表现出更优的计算效率和收敛速度。

改进的随机方差缩减Difference-of-Convex算法的收敛速率

Improved Rates for Stochastic Variance-Reduced Difference-of-Convex Algorithms

提出DCA-PAGE算法，通过结合DCA与PAGE求解结构化非光滑DC规划，在有限和与在线设置下均实现优于现有SVR DCA方法的梯度计算复杂度，并利用间隙函数在更温和假设下获得收敛保证。

High-order Moment Portfolio Optimization via An Accelerated Difference-of-Convex Programming Approach and Sums-of-Squares

The Mean-Variance-Skewness-Kurtosis (MVSK) portfolio optimization model is a quartic nonconvex polynomial minimization problem over a polytope, which can be formulated as a Difference-of-Convex (DC) program. In this manuscript, we investigate four DC programming approaches for solving the MVSK model. First, two DC formulations based on the projective DC decomposition and the Difference-of-Convex-Sums-of-Squares (DC-SOS) decomposition are established, where the second one is novel. Then, DCA is applied to solve these DC formulations. The convergence analysis of DCA for the MVSK model is establi…

Stochastic Difference-of-Convex Algorithms for Solving nonconvex optimization problems

The paper deals with stochastic difference-of-convex functions (DC) programs, that is, optimization problems whose the cost function is a sum of a lower semicontinuous DC function and the expectation of a stochastic DC function with respect to a probability distribution. This class of nonsmooth and nonconvex stochastic optimization problems plays a central role in many practical applications. Although there are many contributions in the context of convex and/or smooth stochastic optimization, algorithms dealing with nonconvex and nonsmooth programs remain rare. In deterministic optimization li…

一种结合凸函数差优化的邻近算法，用于求解一类单比分式规划问题

A proximal algorithm incorporating difference of convex functions optimization for solving a class of single-ratio fractional programming

针对一类可由球面非光滑问题转化而来的单比分式最小化问题，推导最优性条件，提出结合凸函数差优化的PS-DCA算法，证明聚点为临界点及典型问题全局收敛，实验显示其对初值不敏感、不易陷入低质量局部极小值。

凸差分算法的改进收敛速率

Improved convergence rates for the Difference-of-Convex algorithm

本文研究了含弱凸项的凸差分算法（DCA），通过区分八种参数区间精确刻画了单次迭代的目标函数下降，并推导了向临界点收敛的次线性收敛速率，证明了其紧致性。

RA-DCA：面向最大结构DC规划方向稳定性的随机活动集DCA

RA-DCA: A Randomized Active-Set DCA for Directional Stationarity in Max-Structured DC Programs

针对减去项为光滑凸函数有限最大值的非光滑DC规划，提出随机活动集DCA（RA-DCA），通过投影活动梯度到采样方向并检查采样顶点残差，以概率1保证聚点的方向稳定性。

Nesterov's Smoothing Technique and Minimizing Differences of Convex Functions for Hierarchical Clustering

A bilevel hierarchical clustering model is commonly used in designing optimal multicast networks. In this paper, we consider two different formulations of the bilevel hierarchical clustering problem, a discrete optimization problem which can be shown to be NP-hard. Our approach is to reformulate the problem as a continuous optimization problem by making some relaxations on the discreteness conditions. Then Nesterov's smoothing technique and a numerical algorithm for minimizing differences of convex functions called the DCA are applied to cope with the nonsmoothness and nonconvexity of the prob…

求解非光滑最优控制中产生的带互补约束的数学规划问题

Solving mathematical programs with complementarity constraints arising in nonsmooth optimal control

本文针对非光滑最优控制离散化产生的MPCC问题，提出nosbench基准集（含603个问题），系统比较松弛方法、NLP求解器及参数策略，并指出最佳组合仅能求解73.8%的问题，表明MPCC算法与软件仍需改进。

DC半定规划与锥约束DC优化：理论与局部搜索方法

DC Semidefinite Programming and Cone Constrained DC Optimization: Theory and Local Search Methods

本文扩展DC优化理论至锥约束问题，提出DC分解与精确罚DCA方法，并分析其收敛性，应用于压缩模态和球堆积问题。

一种面向不可微函数的非精确增强凸函数差算法

An Inexact Boosted Difference of Convex Algorithm for Nondifferentiable Functions

针对首个DC分量不可微时BDCA方向可能变为上升方向、单调线搜索失效的问题，提出含两个非精确特性的InmBDCA，证明其良定义与聚点临界性，给出迭代复杂度界，实验表明其性能优于nmBDCA和单调DCA。

有界曲率黎曼流形上 Fréchet 回归的近端 DCA

Proximal DCA for Fréchet Regression on Riemannian Manifolds with Bounded Curvature

针对有界截面曲率的完备黎曼流形上的带符号 Fréchet 回归问题，提出基于黎曼近端 DC 算法的 FRIDA 方法，并证明解的存在性、迭代收敛性及复杂度。

A new approach for solving mixed integer DC programs using a continuous relaxation with no integrality gap and smoothing techniques

In this paper, we consider a class of mixed integer programming problems (MIPs) whose objective functions are DC functions, that is, functions representable in terms of the difference of two convex functions. These MIPs contain a very wide class of computationally difficult nonconvex MIPs since the DC functions have powerful expressability. Recently, Maehara, Marumo, and Murota provided a continuous reformulation without integrality gaps for discrete DC programs having only integral variables. They also presented a new algorithm to solve the reformulated problem. Our aim is to extend their res…

基于DC规划的多期风险价值约束投资组合优化

Multi-period Value-at-Risk Constrained Portfolio Optimization via DC Programming

该研究针对带VaR约束等的多期投资组合优化问题，提出iBDCA算法求解，经理论分析与数值实验验证其有效性，可平衡收益、风险等多维度指标。

约束DC问题的不精确MBA方法的收敛性分析

Convergence Analysis of an Inexact MBA Method for Constrained DC Problems

本文针对约束DC优化问题提出一种基于全局误差界的不精确MBA方法，在KL性质下建立完全收敛性、局部收敛速率及迭代复杂度，并通过数值实验验证其在解质量和运行时间上优于DCA-MOSEK。