Primal-Dual Splitting Algorithm for Solving Inclusions with Mixtures of Composite, Lipschitzian, and Parallel-Sum Type Monotone Operators

We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators. An important feature of the algorithm is that the Lipschitzian operators present in the formulation can be processed individually via explicit steps, while the set-valued operators are processed individually via their resolvents. In addition, the algorithm is highly parallel in that most of its steps can be executed simultaneously. This work brings together and notably extends various types of structured monotone inclusion problems and their solution methods. The application to convex minimization problems is given special attention.     

A Simple Primal-Dual Feasible Interior-Point Method for Nonlinear Programming with Monotone Descent

We propose and analyze a primal-dual interior point method of the feasible type, with the additional property that the objective function decreases at each iteration. A distinctive feature of the method is the use of different barrier parameter values for each constraint, with the purpose of better steering the constructed sequence away from non-KKT stationary points. Assets of the proposed scheme include relative simplicity of the algorithm and of the convergence analysis, strong global and local convergence properties, and good performance in preliminary tests. In addition, the initial point is allowed to lie on the boundary of the feasible set.     

Viscosity Results for a Class of Evolution Inclusions with Maximal Monotone Operators

In the finite dimensional setting, we investigate the existence of viscosity subsolutions of Hamilton–Jacobi–Bellman equations related to control problems subject to evolution inclusions governed by time-dependent maximal monotone operators with Young measures.     

Continuous Newton-like Inertial Dynamics for Monotone Inclusions

Set-Valued and Variational Analysis - In a Hilbert framework ℌ, we study the convergence properties of a Newton-like inertial dynamical system governed by a general maximally monotone...     

Nonconvex Differential Inclusions with Nonlinear Monotone Boundary Conditions

Existence results for problems with monotone nonlinear boundary conditions obtained in the previous publications by the author for functional differential equations are transferred to the case of nonconvex differential inclusions with the help of the selection theorem due to A. Bressan and G. Colombo.     

On Maximal Monotone Differential Inclusions in RN

In this paper we consider differential inclusions driven by a maximalmonotone operator. First we show that for the nonconvex system the solutionset viewed as a multifunction of the initial condition admits a continuousselector passing from a prescribed point. Then we use this selector to showthe path connectedness of the solution set. We also investigate thecontinuity properties of the solution multifunction. Finally we solve aviability problem and we also establish the existence of periodic trajectories.     

Evolution Inclusions Governed by Time-Dependent Maximal Monotone Operators with a Full Domain

In this paper, we study the existence of solutions for evolution inclusions governed by time-dependent maximal monotone operators with a full domain. Without assumptions concerning time-regularity on the time-dependent maximal monotone operators, and by using the Moreau-Yosida regularization technique, we establish the existence of solutions in Hilbert spaces. The theoretical result is applied to prove the existence of solutions for semicoercive sweeping processes with velocity constraint.

     

Global Convergence of a Closed-Loop Regularized Newton Method for Solving Monotone Inclusions in Hilbert Spaces

We analyze the global convergence properties of some variants of regularized continuous Newton methods for convex optimization and monotone inclusions in Hilbert spaces. The regularization term is of Levenberg–Marquardt type and acts in an open-loop or closed-loop form. In the open-loop case the regularization term may be of bounded variation.     

Newton-Like Dynamics and Forward-Backward Methods for Structured Monotone Inclusions in Hilbert Spaces

In a Hilbert space setting we introduce dynamical systems, which are linked to Newton and Levenberg–Marquardt methods. They are intended to solve, by splitting methods, inclusions governed by structured monotone operators M=A+B, where A is a general maximal monotone operator, and B is monotone and locally Lipschitz continuous. Based on the Minty representation of A as a Lipschitz manifold, we show that these dynamics can be formulated as differential systems, which are relevant to the Cauchy–Lipschitz theorem, and involve separately B and the resolvents of A. In the convex subdifferential case, by using Lyapunov asymptotic analysis, we prove a descent minimizing property and weak convergence to equilibria of the trajectories. Time discretization of these dynamics gives algorithms combining Newton’s method and forward-backward methods for solving structured monotone inclusions.     

Global Attractors for Multivalued Random Dynamical Systems Generated by Random Differential Inclusions with Multiplicative Noise

In this paper we consider a stochastic differential inclusion with multiplicative noise. It is shown that it generates a multivalued random dynamical system for which there also exists a global random attractor.     

Lyapunov Stability of Differential Inclusions with Lipschitz Cusco Perturbations of Maximal Monotone Operators

Set-Valued and Variational Analysis - We give new criteria for weak and strong invariant closed sets for differential inclusions in $mathbb {R}^{n}$ , and which are simultaneously governed by...     

随机删失下刻度参数的单调经验贝叶斯检验

利用经验贝叶斯方法研究了刻度指数族的两行动问题, 提出了一个在历史样本被随机右删失的条件下收敛速度可以任意接近$O(n^{-1})$的单调经验贝叶斯检验.     

Random Nonlinear Variational Inequalities for Mappings of Monotone Type in Banach Spaces

Abstract

Some new concepts of β-semimonotone, and weakly semiaccretive random mappings are introduced and then some nonlinear variational inequalities for such random mappings are solved.     

实时求解线性规划问题的原对偶神经网络(英文)

本文探讨了线性规划的原问题与对偶问题理论,并在此基础上可开发出一种用于在线求解线性规划的递归神经网络和应用于冗余机器手臂逆运动学的求解问题上.如,Tang等人开展的原对偶神经网络.但鉴于对偶理论的复杂性和多样性,该原对偶神经网络模型仅可以得到线性规划问题的可行解,而本文对该网络模型改进后可得到线性规划问题的最优解.仿真结果证实了这种改进模型在解决线性规划问题上的有效性、正确性和高效率.     

Monotone Approximation of Random Functions with Multivariate Domains in Respect of Lattice Semi-Norms

Consider the problem of approximating a random function which is defined on a compact and convex subset of a topological vector space. For monotone approximation procedures, global and local error bounds with respect to lattice semi-norms are established.     

A New Class of Monotone Mappings and a New Class of Variational Inclusions in Banach Spaces

In this paper, we introduce and study a new class of variational inclusions in Banach spaces. As it concerns the methods of solution, we introduce a new class of monotone mappings. We define a proximal mapping associated with this mappings and show its Lipschitz continuity. By using the technique of proximal mapping, we construct a new iterative algorithm. Under some suitable conditions, we prove the convergence of iterative sequences generated by the algorithm. Our results improve and generalize many known results.     

Random Motion of Strings and Related Stochastic Evolution Equations with Monotone Nonlinearities

Abstract

A limiting problem for a stochastic evolution equation is studied in the paper. In the equation, the linear operator is non-positive with a pure point spectrum, the non-linearity is monotone, and the Brownian motion is cylindrical. It is shown that, in the limit, the mild solution to the evolution equation tends to the solution of an ordinary Ito equation.     

Banach空间中随机微分包含的弱解存在性定理

本文对Banach空间中的微分包含及随机微分包含引入了弱解的概念,并给出了它们的存在性定理。     

随机置换的分量与单调重新构组问题的计算等价性

In this note, it is shown that the monotone reconstruction problem is equi-valent to that of sorting, in the sense of computational complexity. In particular from any given sorting algorithm A, an algorithm B for the monotone reconstruc-tion problem can be developed with at most O(m) time and O( m) space cost more than that used in A, and vice versa. As a consequence of this result, it is obtai-ned that the time complexity of the monotone reconstruction problem of n-ele-ment random permutations is O(nlogn).     

Splittings and Cr-structures for manifolds with nonpositive sectional curvature

Let denote the universal covering space of a compact Riemannian manifold, M ⁿ , with sectional curvature, −1≤K _Mn ≤0. We show that a collection of deck transformations of , satisfying certain (metric dependent) conditions, determines an open dense subset of M ⁿ , at every point of which, there exists a local isometric splitting with nontrivial flat factor. Such a collection, which we call an abelian structure, also gives rise to an essentially canonical Cr-structure in the sense of Buyalo, i.e an atlas for an injective F-structure, for which additional conditions hold. It follows in particular that the minimal volume of M ⁿ vanishes. We show that an abelian structure exists if the injectivity radius at all points of M ⁿ is less than ε(n)>0. This yields a conjecture of Buyalo as well as a strengthened version of the conclusion of Gromov’s “gap conjecture” in our special situation. In addition, we observe that abelian structures on nonpositively curved manifolds have certain stability properties under suitably controlled changes of metric. Oblatum 26-III-1999 & 14-IX-2000?Published online: 8 December 2000