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Model-Based Methods in Derivative-Free Nonsmooth Optimization
Derivative-free optimization (DFO) is the mathematical study of the optimization algorithms that do not use derivatives. One branch of DFO focuses on...
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On Proximal Subgradient Splitting Method for Minimizing the sum of two Nonsmooth Convex Functions
In this paper we present a variant of the proximal forward-backward splitting iteration for solving nonsmooth optimization problems in Hilbert...
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The Proximal Alternating Minimization Algorithm for Two-Block Separable Convex Optimization Problems with Linear Constraints
The Alternating Minimization Algorithm has been proposed by Paul Tseng to solve convex programming problems with two-block separable linear...
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A Gauss–Seidel type inertial proximal alternating linearized minimization for a class of nonconvex optimization problems
In this paper we study a broad class of nonconvex and nonsmooth minimization problems, whose objective function is the sum of a smooth function of...
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Zeros of Sums of Monotone Operators
Properties of the zeros of a single monotone operator were discussed in Section 23.4 . In this chapter, we...
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Proximal Minimization
We saw in Chapter 27 that the solutions to minimization problems can be characterized by fixed point...
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ADMM for monotone operators: convergence analysis and rates
We propose in this paper a unifying scheme for several algorithms from the literature dedicated to the solving of monotone inclusion problems...
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Monotone operator theory in convex optimization
Several aspects of the interplay between monotone operator theory and convex optimization are presented. The crucial role played by monotone...
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Proximal alternating penalty algorithms for nonsmooth constrained convex optimization
We develop two new proximal alternating penalty algorithms to solve a wide range class of constrained convex optimization problems. Our approach...
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A Variant of the Hybrid Proximal Extragradient Method for Solving Strongly Monotone Inclusions and its Complexity Analysis
This paper presents and studies the iteration-complexity of a variant of the hybrid proximal extragradient method for solving inclusion problems with...
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Forward–Partial Inverse–Forward Splitting for Solving Monotone Inclusions
In this paper, we provide a splitting method for finding a zero of the sum of a maximally monotone operator, a Lipschitzian monotone operator, and a...
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An Inertial Tseng’s Type Proximal Algorithm for Nonsmooth and Nonconvex Optimization Problems
We investigate the convergence of a forward–backward–forward proximal-type algorithm with inertial and memory effects when minimizing the sum of a...
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Introduction
The main goal of this chapter is to present a brief overview of operator splitting methods and algorithms when applied to the solution of initial...
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Forward-Backward and Tseng’s Type Penalty Schemes for Monotone Inclusion Problems
We deal with monotone inclusion problems of the form 0 ∈ A x + D x + N C ( x ) in real Hilbert spaces, where A is a maximally monotone operator, D a...
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Two algorithms for solving single-valued variational inequalities and fixed point problems
In this paper, we suggest two new iterative methods for finding a common element of the solution set of a variational inequality problem and the set...
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On Non-dense Orbits of Certain Non-algebraic Dynamical Systems
In this paper, we manage to apply Schmidt games to certain non-algebraic dynamical systems. More precisely, we show that the set of points with...
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A Class of Fejér Convergent Algorithms, Approximate Resolvents and the Hybrid Proximal-Extragradient Method
A new framework for analyzing Fejér convergent algorithms is presented. Using this framework, we define a very general class of Fejér convergent...
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