A short note on solving box inequality and linear equality constrained optimization problem

Rigidity of equality cases in Steiner's perimeter inequality

Characterization results for equality cases and for rigidity of equality cases in Steiner's perimeter inequality are presented. (By rigidity, we mean the situation when all equality cases are vertical translations of the Steiner's symmetral under consideration.) We achieve this through the introduction of a suitable measure-theoretic notion of connectedness and a fine analysis of barycenter functions for sets of finite perimeter having segments as orthogonal sections with respect to an hyperplane.

Kalman Filtering with Equality and Inequality State Constraints

Both constrained and unconstrained optimization problems regularly appear in recursive tracking problems engineers currently address -- however, constraints are rarely exploited for these applications. We define the Kalman Filter and discuss two different approaches to incorporating constraints. Each of these approaches are first applied to equality constraints and then extended to inequality constraints. We discuss methods for dealing with nonlinear constraints and for constraining the state prediction. Finally, some experiments are provided to indicate the usefulness of such methods.

一种结合MADS的罚函数-内点法用于等式和不等式约束优化

A penalty-interior point method combined with MADS for equality and inequality constrained optimization

本文提出了一种结合MADS的罚函数-内点法，用于解决具有等式和不等式约束的非光滑黑箱优化问题，通过改进的罚函数和障碍项策略提升求解效率。

Sequential Quadratic Optimization for Stochastic Optimization with Deterministic Nonlinear Inequality and Equality Constraints

A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is tractable to evaluate constraint function and derivative values in each iteration, but it is intractable to evaluate the objective function or its derivatives in any iteration, and instead an algorithm can only make use of stochastic objective gradient estimates. Under loose assumptions, including that the gradient estimates are unbiased, the algorithm is pro…

Extensions of ADMM for Separable Convex Optimization Problems with Linear Equality or Inequality Constraints

The alternating direction method of multipliers (ADMM) proposed by Glowinski and Marrocco is a benchmark algorithm for two-block separable convex optimization problems with linear equality constraints. It has been modified, specified, and generalized from various perspectives to tackle more concrete or complicated application problems. Despite its versatility and phenomenal popularity, it remains unknown whether or not the ADMM can be extended to separable convex optimization problems with linear inequality constraints. In this paper, we lay down the foundation of how to extend the ADMM to two…

一种面向在线约束优化的控制论方法

A Control Theoretical Approach to Online Constrained Optimization

该研究提出一种基于控制理论的在线约束优化算法，在等式约束下可渐近收敛到最优轨迹，修改后可处理不等式约束的饱和问题，数值实验显示其性能优于现有最优算法。

The equality case in a Poincaré-Wirtinger type inequality

In this paper, generalizing to the non smooth case already existing results, we prove that, for any convex planar set $Ω$, the first non-trivial Neumann eigenvalue $μ_1(Ω)$ of the Hermite operator is greater than or equal to 1. Furthermore, and this is our main result, under some additional assumptions on $Ω$, we show that $μ_1(Ω)=1$ if and only if $Ω$ is any strip. The study of the equality case requires, among other things, an asymptotic analysis of the eigenvalues of the Hermite operator in thin domains.

无目标函数算法用于非凸随机优化问题中的确定性等式和不等式约束

An objective-function-free algorithm for nonconvex stochastic optimization with deterministic equality and inequality constraints

本文提出一种无目标函数算法，用于解决具有随机目标和确定性等式和不等式约束的优化问题。该算法通过自适应选择函数减少和约束改善迭代，采用Adagrad型步长，证明在全秩雅可比问题中，联合对偶最优度量以O(1/sqrt{k})速率收敛。

一类带等式与盒约束优化问题的加速算法

Accelerated Algorithms for a Class of Optimization Problems with Equality and Box Constraints

本文针对带等式与盒约束的凸优化问题，提出一种引入时变增益的新型高阶调节器，在保证约束任意时刻可行的同时实现加速收敛，并用数值例子验证理论结果。

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

Steering exact penalty DCA for nonsmooth DC optimization problems with equality and inequality constraints

提出一种基于ℓ1罚函数和自适应罚参数更新策略的DCA变体，用于求解带非光滑DC等式与不等式约束的优化问题，并通过收敛性分析和两个离散最优控制算例验证其有效性。

Stability Analysis of Time-varying Delay Neural Network for Convex Quadratic Programming With Equality Constraints and Inequality Constraints

In this paper, a kind of neural network with time-varying delays is proposed to solve the problems of quadratic programming. The delay term of the neural network changes with time t. The number of neurons in the neural network is n + h, so the structure is more concise. The equilibrium point of the neural network is consistent with the optimal solution of the original optimization problem. The existence and uniqueness of the equilibrium point of the neural network are proved. Application inequality technique proved global exponential stability of the network. Some numerical examples are given …

Optimization with Equality and Inequality Constraints Using Parameter Continuation

We generalize the successive continuation paradigm introduced by Kernévez and Doedel [16] for locating locally optimal solutions of constrained optimization problems to the case of simultaneous equality and inequality constraints. The analysis shows that potential optima may be found at the end of a sequence of easily-initialized separate stages of continuation, without the need to seed the first stage of continuation with nonzero values for the corresponding Lagrange multipliers. A key enabler of the proposed generalization is the use of complementarity functions to define relaxed complementa…

一种用于带等式与不等式约束非凸优化的近端增广拉格朗日方法

A proximal augmented Lagrangian method for nonconvex optimization with equality and inequality constraints

提出一种不精确近端增广拉格朗日方法，通过自适应更新惩罚参数和近端项，加速收敛并改善病态，理论分析及数值实验验证了其有效性。

Existence Result for Generalized Variational Equality

In this paper, we prove the existence of a solution to the Stampachia variational inequality under weakened assumptions on the given operator. As a consequence, we provide some sufficient conditions that under them the generalized equation $0\in T(x)$ has a solution. Furthermore, by using generalized results of continuity and monotonicity, we extend the related existence results and we answer an open problem proposed by Kassay and Miholka (J Optim Theory Appl 159 (2013) 721-740).