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Recent Developments on Primal–Dual Splitting Methods with Applications to Convex Minimization
This chapter presents a survey on primal–dual splitting methods for solving monotone inclusion problems involving maximally monotone operators,...
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Keynote Iterative Methods
In this chapter we give an introduction to the basic (sub)gradient-based methods for minimizing a convex function on a Hilbert space. We pay special...
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Split Feasibility and Fixed Point Problems
In this survey article, we present an introduction of split feasibility problems, multisets split feasibility problems and fixed point problems. The...
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Iteration-complexity of first-order penalty methods for convex programming
This paper considers a special but broad class of convex programming problems whose feasible region is a simple compact convex set intersected with...
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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 first characterize the zeros of sums of...
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Templates for convex cone problems with applications to sparse signal recovery
This paper develops a general framework for solving a variety of convex cone problems that frequently arise in signal processing, machine learning,...
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Proximal Minimization
As seen in Chapter 26, the solutions to variational problems can be characterized by fixed point equations involving proximity operators. Since...
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A family of projective splitting methods for the sum of two maximal monotone operators
A splitting method for two monotone operators A and B is an algorithm that attempts to converge to a zero of the sum A + B by solving a sequence of...
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Self-adaptive operator splitting methods for monotone variational inequalities
Solving a variational inequality problem VI(Ω, F ) is equivalent to finding a solution of a system of nonsmooth equations (a hard problem). The...
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Auxiliary Problem Principle and Proximal Point Methods
An extension of the auxiliary problem principle to variational inequalities with non-symmetric multi-valued operators in Hilbert spaces is studied....
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A Hybrid Approximate Extragradient – Proximal Point Algorithm Using the Enlargement of a Maximal Monotone Operator
We propose a modification of the classical extragradient and proximal point algorithms for finding a zero of a maximal monotone operator in a Hilbert...