Jirong Yi
Inspired by alternating direction method of multipliers and the idea of operator splitting, we propose a efficient algorithm for solving large-scale quadratically constrained basis pursuit. Experimental results show that the proposed algorithm can achieve 50~~100 times speedup when compared with the baseline interior point algorithm implemented in CVX.
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Algorithms based on the hard thresholding principle have been well studied with sounding theoretical guarantees in the compressed sensing and more general sparsity-constrained optimization. It is widely observed in existing empirical studies that when a restricted Newton step was used (as the debiasing step), the hard-thresholding algorithms tend to meet halting conditions in a significantly low number of iterations and are very efficient. Hence, the thus obtained Newton hard-thresholding algorithms call for stronger theoretical guarantees than for their simple hard-thresholding counterparts. …
Phase Retrieval Using Feasible Point Pursuit: Algorithms and Cramér-Rao Bound
本文提出两种基于非凸二次约束二次规划的相位恢复算法，并推导了Cramér-Rao界，通过仿真显示LS-FPP在性能上优于现有算法并接近Cramér-Rao界。
Efficient Algorithms for Robust and Stable Principal Component Pursuit Problems
鲁棒主成分分析（Robust Principal Component Analysis，RPCA）是从一组含有稀疏粗差的观测值中恢复低秩矩阵的方法，在计算机视觉、图像处理和网络数据排序等领域有着广泛的应用。在一定条件下，NP难RPCA问题的解可以通过求解一个凸优化问题，即鲁棒主元追踪（RPCP）来得到。此外，如果观察到的数据矩阵也被破坏的密集噪声矩阵，除了粗稀疏误差，然后稳定的主成分追踪（SPCP）问题的解决，以恢复低秩矩阵。在本文中，我们开发了有效的算法与可证明的迭代复杂性界解决RPCP和SPCP。对数百万变量和约束条件的问题（如从监控视频中提取前景，从人脸图像中去除阴影和镜面反射以及从严重损坏的数据中去除视频去噪）的数值结果表明，我们的算法在精度和速度方面与当前最先进的RPCP和SPCP求解器具有竞争力。
Hard-thresholding-based algorithms have seen various advantages for sparse optimization in controlling the sparsity and allowing for fast computation. Recent research shows that when techniques of the Newton-type methods are integrated, their numerical performance can be improved surprisingly. This paper develops a gradient projection Newton pursuit algorithm that mainly adopts the hard-thresholding operator and employs the Newton pursuit only when certain conditions are satisfied. The proposed algorithm is capable of converging globally and quadratically under the standard assumptions. When i…
Recent methods for learning a linear subspace from data corrupted by outliers are based on convex $\ell_1$ and nuclear norm optimization and require the dimension of the subspace and the number of outliers to be sufficiently small. In sharp contrast, the recently proposed Dual Principal Component Pursuit (DPCP) method can provably handle subspaces of high dimension by solving a non-convex $\ell_1$ optimization problem on the sphere. However, its geometric analysis is based on quantities that are difficult to interpret and are not amenable to statistical analysis. In this paper we provide a ref…
The aim of structured optimization is to assemble a solution, using a given set of (possibly uncountably infinite) atoms, to fit a model to data. A two-stage algorithm based on gauge duality and bundle method is proposed. The first stage discovers the optimal atomic support for the primal problem by solving a sequence of approximations of the dual problem using a bundle-type method. The second stage recovers the approximate primal solution using the atoms discovered in the first stage. The overall approach leads to implementable and efficient algorithms for large problems.
Alternating minimization for square root principal component pursuit
针对平方根主成分追踪（SRPCP）的计算难题，本文提出无需调参的AltMin算法，并结合核范数变分表述与Burer-Monteiro分解加速，实验验证其高效鲁棒。
An ADMM algorithm for solving a proximal bound-constrained quadratic program
考虑了一个由二次函数给出的近似算子，并给出了一个利用乘子交替方向法（ADMM）的优化算法。该算法是特别有效的，以解决一个集合的邻近运营商共享相同的二次型，或者如果二次规划是一个二进制二次问题的松弛。
Asynchronous Algorithms for Solving Linear Programs
在本文中，我们设计和分析算法异步求解线性规划使用非线性信号处理结构。特别是，我们讨论了一个一般的程序，用于生成这些结构，使结构的不动点是在一个变化的基础上的最小化相关联的线性规划。我们讨论的方法组织成分布式实现的计算，并提供了一个治疗的收敛。所提出的算法伴随着切比雪夫中心和基追踪问题的数值模拟。
Semidefinite programs (SDP) are important in learning and combinatorial optimization with numerous applications. In pursuit of low-rank solutions and low complexity algorithms, we consider the Burer--Monteiro factorization approach for solving SDPs. We show that all approximate local optima are global optima for the penalty formulation of appropriately rank-constrained SDPs as long as the number of constraints scales sub-quadratically with the desired rank of the optimal solution. Our result is based on a simple penalty function formulation of the rank-constrained SDP along with a smoothed ana…
An Efficient Solution Method for Solving Convex Separable Quadratic Optimization Problems
本文基于KKT系统的迭代求解方案，提出一种求解带多凸可分约束的二次规划问题的高效方法，证明其等价于对偶坐标上升算法，且数值实验表明其在大规模问题上优于Gurobi求解器。
Distributed Basis Pursuit
针对基追踪（BP）优化问题，提出一种分布式算法D-ADMM，通过交替方向乘子法在传感器网络等分布式平台上实现，显著减少节点间通信。
We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We demonstrate the use of our method on a small, motivating example and present the results of a small number of computational tests demonstrating its utility for larger scale problems.
A Computational Procedure for solving a Non-Convex Multi-Objective Quadratic Programming under Fuzzy Environment
研究了一类非凸模糊多目标二次规划问题，其中工艺参数和资源参数均为模糊，隶属函数为非线性。一个计算程序，以找到一个模糊有效解这个问题的发展。最后给出了一个数值例子来说明该方法。
We develop procedures, based on minimization of the composition $f(x) = h(c(x))$ of a convex function $h$ and smooth function $c$, for solving random collections of quadratic equalities, applying our methodology to phase retrieval problems. We show that the prox-linear algorithm we develop can solve phase retrieval problems---even with adversarially faulty measurements---with high probability as soon as the number of measurements $m$ is a constant factor larger than the dimension $n$ of the signal to be recovered. The algorithm requires essentially no tuning---it consists of solving a sequence…
A new algorithm for solving the solution of the linear-quadratic optimization problem (LQP) with unseparated boundary conditions in the continuous case is given. Using the properties of symmetry of the corresponding Hamiltonian matrix, the Euler-Lagrange equations, it is shown that linear algebraic equations for determining the missing initial data of the system being solved have a symmetric principal matrix. The results are illustrated by the example of LQP optimization (stationary case) with minimal control actions.
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the quadratic shortest path problem with a matrix variable of order $m+1$, where $m$ is the number of arcs in the graph. We use the alternating direction method of multipliers to solve the semidefinite programming relaxations. Numerical results show that our bounds are currently the strongest bounds for the quadratic shortest path problem. We also present comput…
Recovering a low-rank matrix from highly corrupted measurements arises in compressed sensing of structured high-dimensional signals (e.g., videos and hyperspectral images among others). Robust principal component analysis (RPCA), solved via principal component pursuit (PCP), recovers a low-rank matrix from sparse corruptions that are of unknown value and support by decomposing the observation matrix into two terms: a low-rank matrix and a sparse one, accounting for sparse noise and outliers. In the more general setting, where only a fraction of the data matrix has been observed, low-rank matri…
The greedy side of the LASSO: New algorithms for weighted sparse recovery via loss function-based orthogonal matching pursuit
本文提出基于损失函数推广 OMP 的加权稀疏恢复贪婪算法，给出多种加权 LASSO 形式的显式选择规则，并通过实验验证其继承 SR-LASSO 与 LAD-LASSO 的优良特性。
An Alternating Direction Method with Increasing Penalty for Stable Principal Component Pursuit
稳定主元追踪（Stable Principal Component Pursuit，SPCP）是一个非光滑的凸优化问题，它的解使得即使只有一小部分数据是可观测的，也能可靠地恢复被密集噪声矩阵破坏的数据矩阵的低秩和稀疏分量。本文提出了一种求解SPCP的新算法。该算法是一个修改的交替方向法的乘法器（ADMM），我们使用一个递增序列的罚参数，而不是一个固定的罚款。该算法是基于部分变量分裂和工作直接与非光滑目标函数。我们证明了原始序列和对偶序列在罚参数序列上在较弱的条件下收敛。据我们所知，这是第一个收敛结果的可变罚款ADMM时，罚款是没有界的，目标函数是非光滑的，它的次微分不是一致有界的。使用部分变量分裂和采用递增序列的惩罚乘数，一起，显着减少所需的迭代次数，以实现实际的可行性。我们的初步计算测试表明，该算法在实践中非常好，并优于ASALM，一个国家的最先进的ADMM算法的SPCP问题与一个常数罚参数。
In this paper, we propose a two-phase algorithm for solving continuous rank-one quadratic knapsack problems (R1QKP). In particular, we study the solution structure of the problem without the knapsack constraint. We propose an $O(n\log n)$ algorithm in this case. We then use the solution structure to propose an $O(n^2\log n)$ algorithm that finds an interval containing the optimal value of the Lagrangian dual of R1QKP. In the second phase, we solve the restricted Lagrangian dual problem using a traditional single-variable optimization method. We perform a computational test on random instances …
Ordinary differential equations that model technical systems often contain states, that are considered dangerous for the system. A trajectory that reaches such a state usually indicates a flaw in the design. In this paper, we present and study the properties of an algorithm for finding such trajectories. That is, for a given ordinary differential equation, the algorithm finds a trajectory that originates in one set of states and reaches another one. The algorithm is based on sequential quadratic programming applied to a regularized optimization problem obtained by multiple shooting.
This paper analyzes the iteration-complexity of a quadratic penalty accelerated inexact proximal point method for solving linearly constrained nonconvex composite programs. More specifically, the objective function is of the form $f + h$ where $f$ is a differentiable function whose gradient is Lipschitz continuous and $h$ is a closed convex function with bounded domain. The method, basically, consists of applying an accelerated inexact proximal point method for solving approximately a sequence of quadratic penalized subproblems associated to the linearly constrained problem. Each subproblem of…
Quantum adiabatic evolution is perceived as useful for binary quadratic programming problems that are a priori unconstrained. For constrained problems, it is a common practice to relax linear equality constraints as penalty terms in the objective function. However, there has not yet been proposed a method for efficiently dealing with inequality constraints using the quantum adiabatic approach. In this paper, we give a method for solving the Lagrangian dual of a binary quadratic programming (BQP) problem in the presence of inequality constraints and employ this procedure within a branch-and-bou…
Doubly nonnegative relaxation method for solving multiple objective quadratic programming problems
多目标优化和帕累托最优是经济学中的基本工具。本文提出了一种求解多目标二次规划问题的新松弛法。利用线性加权和方法，将多目标二次规划问题转化为单目标问题。由于这类单目标二次规划问题在一般情况下仍是非凸的和NP-难的。分别利用提升技术和双重非负松弛技术，将该单目标二次规划问题转化为可计算的凸双重非负规划问题。在较弱的条件下，该可计算凸问题的最优解是原问题的（弱）Pareto最优解.最后，通过两个算例和一个实际的投资组合问题对所提出的方法进行了验证.测试问题的解决\texttt{CVX}包，这是一个求解器的凸优化。数值结果表明，该方法是有效的，具有一定的应用前景.
Best Subset Selection: Optimal Pursuit for Feature Selection and Elimination
本文从优化角度提出特征选择与剔除的新准则，通过精确求解优化子问题生成增强的最优子集选择算法，在不增加计算成本下于压缩感知等任务取得显著增益。
Solving Monotone Linear-Quadratic Generalized Nash Equilibrium Problems via Quadratic Programming
该研究针对带凸二次成本与共享仿射约束的N参与者单调线性二次广义纳什均衡问题，通过将其转化为二次规划，提出两种加速算法，实验表明所提方法性能优于现有方法。
An Algorithm for Solving Quadratic Optimization Problems with Nonlinear Equality Constraints
本文提出一种高效算法求解带非线性等式约束的二次优化问题，证明其局部收敛性，并通过椭圆拟合和电机状态参考生成应用验证其有效性。
We consider the problem of maximizing the $\ell_1$ norm of a linear map over the sphere, which arises in various machine learning applications such as orthogonal dictionary learning (ODL) and robust subspace recovery (RSR). The problem is numerically challenging due to its nonsmooth objective and nonconvex constraint, and its algorithmic aspects have not been well explored. In this paper, we show how the manifold structure of the sphere can be exploited to design fast algorithms for tackling this problem. Specifically, our contribution is threefold. First, we present a manifold proximal point …
Mathematical programs with complementarity constraints are notoriously difficult to solve due to their nonconvexity and lack of constraint qualifications in every feasible point. This work focuses on the subclass of quadratic programs with linear complementarity constraints. A novel approach to solving a penalty reformulation using sequential convex programming and a homotopy on the penalty parameter is introduced. Linearizing the necessarily nonconvex penalty function yields convex quadratic subproblems, which have a constant Hessian matrix throughout all iterates. This allows solution comput…
Error analysis of approximation algorithm for standard bi-quadratic programming
考虑了NP-困难的标准双二次规划（StBQP）的近似求解问题。在将原问题转化为等价的共正张量规划后，我们展示了如何通过一系列的多面体锥来近似共正张量的锥来近似最优解。所建立的逼近质量表明，存在求解StBQP的多项式时间逼近方案（PTAS），并可推广到求解标准的多重二次规划.一些数值例子来说明我们的方法。
An Improved Sequential Quadratic Programming Algorithm for Solving General Nonlinear Programming Problems
本文讨论了一类带有不等式和等式约束的一般非线性规划问题。首先，将原问题转化为一个仅含不等式约束的简单等价问题。然后，受序列二次规划（SQP）方法和线性方程组（SLE）方法思想的启发，提出了一种求解原问题的新型SQP算法。在每次迭代中，搜索方向由两个方向的组合产生，这两个方向分别通过求解总是可行的二次规划（QP）子问题和SLE获得。为了克服Maratos效应，通过求解另一个系统方程组得到高阶修正方向。这两个SLE具有相同的系数矩阵，并且我们只需要在有限次迭代之后求解其中一个。通过一种新的线搜索技术，在适当的假设条件下，该算法具有全局收敛性和超线性收敛性。最后，一些比较数值结果表明，该算法是有效的和有前途的。
Sum of Squares Basis Pursuit with Linear and Second Order Cone Programming
本文提出通过迭代求解线性或二次锥规划来近似半正定或平方和规划的最优值，利用DSOS和SDSOS多项式改进界，并应用于独立集和划分问题。
- In this paper we introduce a new method to solve fixed-delay optimal control problems which exploits numerical homotopy procedures. It is known that solving this kind of problems via indirect methods is complex and computationally demanding because their implementation is faced with two difficulties: the extremal equations are of mixed type, and besides, the shooting method has to be carefully initialized. Here, starting from the solution of the non-delayed version of the optimal control problem, the delay is introduced by numerical homotopy methods. Convergence results, which ensure the eff…
We propose a data-driven framework for efficiently solving quadratic programming (QP) problems by reducing the number of variables in high-dimensional QPs using instance-specific projection. A graph neural network-based model is designed to generate projections tailored to each QP instance, enabling us to produce high-quality solutions even for previously unseen problems. The model is trained on heterogeneous QPs to minimize the expected objective value evaluated on the projected solutions. This is formulated as a bilevel optimization problem; the inner optimization solves the QP under a given…
The time-varying quadratic miniaturization (TVQM) problem, as a hotspot currently, urgently demands a more reliable and faster--solving model. To this end, a novel adaptive coefficient constructs framework is presented and realized to improve the performance of the solution model, leading to the adaptive zeroing-type neural dynamics (AZTND) model. Then the AZTND model is applied to solve the TVQM problem. The adaptive coefficients can adjust the step size of the model online so that the solution model converges faster. At the same time, the integration term develops to enhance the robustness o…
A stochastic linear quadratic (LQ) optimal control problem with a pointwise linear equality constraint on the terminal state is considered. A strong Lagrangian duality theorem is proved under a uniform convexity condition on the cost functional and a surjectivity condition on the linear constraint mapping. Based on the Lagrangian duality, two approaches are proposed to solve the constrained stochastic LQ problem. First, a theoretical method is given to construct the closed-form solution by the strong duality. Second, an iterative algorithm, called augmented Lagrangian method (ALM), is proposed…
We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are characterized by a small total number of active constraints and by low-rank constraint matrices. We exploit this special structure by solving the dual problem, using a barrier method in combination with a coordinate-wise exact line search. The main ingredient of our algorithm is the computationally cheap update at each iteration and an easy computation of the exact step size. Compared to interior point methods, our appro…
We derive Nash equilibria for a class of quadratic multi-leader-follower games using the nonsmooth best response function. To overcome the challenge of nonsmoothness, we pursue a smoothing approach resulting in a reformulation as a smooth Nash equilibrium problem. The existence and uniqueness of solutions are proven for all smoothing parameters. Accumulation points of Nash equilibria exist for a decreasing sequence of these smoothing parameters and we show that these candidates fulfill the conditions of s-stationarity and are Nash equilibria to the multi-leader-follower game. Finally, we propo…
In this paper, we discuss the solution of a Quadratic Eigenvalue Complementarity Problem (QEiCP) by using Difference of Convex (DC) programming approaches. We first show that QEiCP can be represented as dc programming problem. Then we investigate different dc programming formulations of QEiCP and discuss their dc algorithms based on a well-known method -- DCA. A new local dc decomposition is proposed which aims at constructing a better dc decomposition regarding to the specific feature of the target problem in some neighborhoods of the iterates. This new procedure yields faster convergence and…
Fix and Bound: An efficient approach for solving large-scale quadratic programming problems with box constraints
本文提出一种结合半定规划界与最优性线性割的分支定界算法，通过变量固定缩减规模，高效求解大规模盒约束非凸二次规划，实验表明其达到最先进水平。
Solving Indefinite Quadratic Programs by Dynamical Systems: Preliminary Investigations
本文用动力系统求解不定二次规划，证明了全局解存在唯一性，分析了强伪单调性，并建立了轨迹收敛到KKT点的结果。
Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause inconveniences when solutions are used for rigorous reasoning. We contribute on three levels to overcome this issue. First, we present a novel refinement algorithm to solve QPs to arbitrary precision. It iteratively solves refined QPs, assuming a floating-point QP solver oracle. We prove linear convergence of residuals and primal errors. Second, we provide an ef…
We propose a new formulation of quadratic optimization problems. The objective function $F(f(x),g(x))$ is given as composition of a quadratic function $F(z)$ with two $n$-variate quadratic functions $z_1=f(x)$ and $z_2=g(x).$ In addition, it incorporates with a set of linear inequality constraints in $z=(z_1,z_2)^T,$ while having an implicit constraint that $z$ belongs to the joint numerical range of $(f,g).$ The formulation is very general in the sense that it covers quadratic programming with a single quadratic constraint of all types, including the inequality-type, the equality-type, and th…
GPU-Accelerated Sequential Quadratic Programming Algorithm for Solving ACOPF
本研究开发了一种基于GPU并行计算的SQP算法，通过ADMM分解ACOPF的二次规划子问题，在较大规模算例中显著缩短了求解时间。
A New Global Optimization Method Based on Simplex Branching for Solving a Class of Non-Convex QCQP Problems
本文针对具有凸二次约束的非凸二次规划问题，通过重构为等价问题，提出基于分支定界框架的全局优化算法，结合松弛与外部逼近技术，确保全局最优性并分析理论可行性。
SuperADMM: Solving Quadratic Programs Faster with Dynamic Weighting ADMM
本研究提出加速ADMM算法superADMM，通过单约束动态加权迭代更新求解二次规划，配套稳定性分析与参数调优方法，C语言实现支持多语言调用，性能优于现有主流求解器。
A Douglas-Rachford Splitting Method for Solving Monotone Variational Inequalities in Linear-quadratic Dynamic Games
本文提出一种求解线性二次动态博弈中单调变分不等式的Douglas-Rachford分裂方法，该方法具有线性收敛速度，适用于递推控制架构，并通过自动驾驶应用的数值实验验证了其有效性。
An adaptive discretization method solving semi-infinite optimization problems with quadratic rate of convergence
针对半无限优化问题求解难度高的问题，结合经典自适应离散化与双层优化技术，提出一种具二次收敛速度的新方法，并证明迭代极限为驻点。
An Outer Approximation Method for Solving Mixed-Integer Convex Quadratic Programs with Indicators
针对带指示变量的混合整数凸二次规划，本文提出从多种凸松弛构造割平面的新技术并形成大规模外逼近算法，在稀疏投资组合选择问题上显著优于现有方法。
Solving Convex Quadratic Optimization with Indicators Over Structured Graphs
本文提出了一种在结构图上求解带有指示符的凸二次优化问题的算法，通过动态规划和结构条件优化，实现线性复杂度，并在预测和异常检测中展示了优越性能。
A semi-smooth Newton method for solving convex quadratic programming problem under simplicial cone constraint
研究了单纯锥约束凸二次规划问题。该问题的最优性条件是一个线性互补性问题。在适当的条件下，这一事实导致了单纯锥约束凸二次规划问题与非光滑方程组的唯一解问题的等价性.它表明，半光滑牛顿法适用于这个非光滑的方程组总是定义良好，并在一个温和的假设下，单纯锥的方法产生一个序列，线性收敛到它的解决方案。此外，我们还证明了生成序列对任意起点是有界的，并给出了该序列的任意聚点的计算公式。数值结果表明，这种方法实现了精确的解决方案，在几个迭代大的问题。
The alternating direction method of multipliers (ADMM) is a widely used method for solving many convex minimization models arising in signal and image processing. In this paper, we propose an inertial ADMM for solving a two-block separable convex minimization problem with linear equality constraints. This algorithm is obtained by making use of the inertial Douglas-Rachford splitting algorithm to the corresponding dual of the primal problem. We study the convergence analysis of the proposed algorithm in infinite-dimensional Hilbert spaces. Furthermore, we apply the proposed algorithm on the rob…
We present a numerical method for the minimization of objectives that are augmented with large quadratic penalties of overdetermined inconsistent equality constraints. Such objectives arise from quadratic integral penalty methods for the direct transcription of equality constrained optimal control problems. The Augmented Lagrangian Method (ALM) has a number of advantages over the Quadratic Penalty Method (QPM) for solving this class of problems. However, if the equality constraints of the discretization are inconsistent, then ALM might not converge to a point that minimizes the unconstrained b…
The solution of a constrained linear-quadratic regulator problem is determined by the set of its optimal active sets. We propose an algorithm that constructs this set of active sets for a desired horizon N from that for horizon N-1. While it is not obvious how to extend the optimal feedback law itself for horizon N-1 to horizon N, a simple relation between the optimal active sets for two successive horizon lengths exists. Specifically, every optimal active set for horizon N is a superset of an optimal active set for horizon N-1 if the constraints are ordered stage by stage. The stagewise treat…
Solving Linear-Quadratic Stochastic Control Problems with Signatures
本文提出一种基于签名的数值方法，用于高效求解多维线性二次随机控制问题，通过将问题转化为确定性凸优化并验证截断签名的有效性，实现了高精度的数值结果。
Solving quadratic systems of equations in n variables and m measurements of the form $y_i = |a^T_i x|^2$ , $i = 1, ..., m$ and $x \in R^n$ , which is also known as phase retrieval, is a hard nonconvex problem. In the case of standard Gaussian measurement vectors, the wirtinger flow algorithm Chen and Candes (2015) is an efficient solution. In this paper, we proposed a new form of wirtinger flow and a new spectral initialization method based on this new algorithm. We proved that the new wirtinger flow and initialization method achieve linear sample and computational complexities. We further ext…
We present algorithm MIQCR-CB that is an advancement of method MIQCR~(Billionnet, Elloumi and Lambert, 2012). MIQCR is a method for solving mixed-integer quadratic programs and works in two phases: the first phase determines an equivalent quadratic formulation with a convex objective function by solving a semidefinite problem $(SDP)$, and, in the second phase, the equivalent formulation is solved by a standard solver. As the reformulation relies on the solution of a large-scale semidefinite program, it is not tractable by existing semidefinite solvers, already for medium sized problems. To sur…
Sequential Quadratic Optimization for Solving Expectation Equality Constrained Stochastic Optimization Problems
本文提出一种顺序二次规划方法，用于求解带有期望等式约束的非线性随机优化问题，通过自适应步长策略和梯度估计实现迭代更新，并分析了算法的收敛性及复杂度。
Solving Quadratic Programs with Slack Variables via ADMM without Increasing the Problem Size
本文提出一种简单的ADMM方法，用于求解带松弛变量的二次规划问题，不增加原始问题规模，通过调整z更新的投影实现，证明其等价于应用ADMM到带有松弛变量的QP，实验显示方法更高效。
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