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In this paper, we consider the problem of finding an almost surely common fixed point of a family of paracontraction maps indexed on a probability space, which we refer to as the stochastic feasibility problem. We show that a random…

Dynamical Systems · Mathematics 2020-08-12 Edgar Matias , Majela Pentón Machado

We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…

Optimization and Control · Mathematics 2020-05-29 Rohit Kannan , James Luedtke

The subdivision algorithm by Dellnitz and Hohmann for the computation of invariant sets of dynamical systems decomposes the relevant region of the state space into boxes and analyzes the induced box dynamics. Its convergence is proved in an…

Numerical Analysis · Mathematics 2017-08-15 Janosch Rieger

We introduce a new system of split variational inequality problems which is a natural extension of split variational inequality problem in semi-inner product spaces. We use the retraction technique to propose an iterative algorithm for…

Functional Analysis · Mathematics 2017-01-20 K. R. Kazmi , Mohd Furkan

A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit…

Optimization and Control · Mathematics 2013-03-04 Stephen Becker , M. Jalal Fadili

This paper is based on Tseng's exgradient algorithm for solving variational inequality problems in real Hilbert spaces. Under the assumptions that the cost operator is quasimonotone and Lipschitz continuous, we establish the strong…

Optimization and Control · Mathematics 2026-01-14 Meiying Wang , Hongwei Liu , Jun Yang

We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous…

Optimization and Control · Mathematics 2015-12-31 J. Y. Bello Cruz , R. Diaz Millan

We provide a comprehensive study of the convergence of the forward-backward algorithm under suitable geometric conditions, such as conditioning or {\L}ojasiewicz properties. These geometrical notions are usually local by nature, and may…

Optimization and Control · Mathematics 2023-12-25 Guillaume Garrigos , Lorenzo Rosasco , Silvia Villa

A general primal-dual splitting algorithm for solving systems of structured coupled monotone inclusions in Hilbert spaces is introduced and its asymptotic behavior is analyzed. Each inclusion in the primal system features compositions with…

Optimization and Control · Mathematics 2013-02-14 Patrick L. Combettes

Backpropagation is the pivotal algorithm underpinning the success of artificial neural networks, yet it has critical limitations such as biologically implausible backward locking and global error propagation. To circumvent these…

Machine Learning · Computer Science 2025-09-11 James Gong , Raymond Luo , Emma Wang , Leon Ge , Bruce Li , Felix Marattukalam , Waleed Abdulla

We propose in this paper a unifying scheme for several algorithms from the literature dedicated to the solving of monotone inclusion problems involving compositions with linear continuous operators in infinite dimensional Hilbert spaces. We…

Optimization and Control · Mathematics 2017-05-08 Radu Ioan Bot , Ernö Robert Csetnek

This letter investigates the convergence and concentration properties of the Stochastic Mirror Descent (SMD) algorithm utilizing biased stochastic subgradients. We establish the almost sure convergence of the algorithm's iterates under the…

Optimization and Control · Mathematics 2024-07-09 Anik Kumar Paul , Arun D Mahindrakar , Rachel K Kalaimani

In this article, we study the convergence of algorithms for solving monotone inclusions in the presence of adjoint mismatch. The adjoint mismatch arises when the adjoint of a linear operator is replaced by an approximation, due to…

Optimization and Control · Mathematics 2023-11-10 Emilie Chouzenoux , Jean-Christophe Pesquet , Fernando Roldán

In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…

Functional Analysis · Mathematics 2010-10-26 Kristian Bredies , Dirk A. Lorenz

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…

Optimization and Control · Mathematics 2011-08-09 Patrick L. Combettes , Jean-Christophe Pesquet

We introduce a forward-backward-forward (FBF) algorithm for solving bilevel equilibrium problem associated with bifunctions on a real Hilbert space. This modifies the forward-backward algorithm by relaxing cocoercivity with monotone and…

Optimization and Control · Mathematics 2024-03-19 Kanchan Mittal , Pankaj Gautam , V. Vetrivel

In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…

Machine Learning · Computer Science 2016-11-17 Luo Luo , Zihao Chen , Zhihua Zhang , Wu-Jun Li

We present a notion of almost periodicity wich can be applied to random dynamical systems as well as almost periodic stochastic differential equations in Hilbert spaces (abstract stochastic partial differential equations). This concept…

Dynamical Systems · Mathematics 2020-03-17 Paul Raynaud de Fitte

In real applications, the construction of prior and acceleration of sampling for posterior are usually two key points of Bayesian inversion algorithm for engineers. In this paper, q-analogy of Gaussian distribution, q-Gaussian distribution,…

Numerical Analysis · Mathematics 2018-08-06 Zhiliang Deng , Xiaomei Yang

In the paper, we introduce several accelerate iterative algorithms for solving the multiple-set split common fixed-point problem of quasi-nonexpansive operators in real Hilbert space. Based on primal-dual method, we construct several…

Optimization and Control · Mathematics 2023-06-08 Chenzheng Guo , Jing Zhao