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In this paper, we introduce an inexact approach to the Boosted Difference of Convex Functions Algorithm (BDCA) for solving nonconvex and nondifferentiable problems involving the difference of two convex functions (DC functions). Specifically, when th
Externí odkaz:
http://arxiv.org/abs/2412.05697
The problem of minimizing the difference of two lower semicontinuous, proper, convex functions (a DC function) on a nonempty closed convex set in a locally convex Hausdorff topological vector space is studied in this paper. The focus is made on the s
Externí odkaz:
http://arxiv.org/abs/2411.19272
The scaled relative graph (SRG) is a powerful graphical tool for analyzing the properties of operators, by mapping their graph onto the complex plane. In this work, we study the SRG of two classes of nonmonotone operators, namely the general class of
Externí odkaz:
http://arxiv.org/abs/2411.17419
By applying some techniques of set-valued and variational analysis, we study solution stability of nonhomogeneous split equality problems and nonhomogeneous split feasibility problems, where the constraint sets need not be convex. Necessary and suffi
Externí odkaz:
http://arxiv.org/abs/2411.11019
In this paper we provide an efficient computation of the projection onto the cone generated by the epigraph of the perspective of any convex lower semicontinuous function. Our formula requires solving only two scalar equations involving the proximity
Externí odkaz:
http://arxiv.org/abs/2411.08000
Autor:
Gfrerer, Helmut
We will show that a multifunction is strictly proto-differentiable at a point of its graph if and only if it is graphically strictly differentiable, i.e., the graph of the multifunction locally coincides, up to a change of coordinates, with the graph
Externí odkaz:
http://arxiv.org/abs/2411.01346
Autor:
Roubal, Tomáš, Valdman, Jan
This paper investigates a path-following method inspired by the semismooth$^*$ approach for solving algebraic inclusions, with a primary emphasis on the role of uniform subregularity. Uniform subregularity is crucial for ensuring the robustness and s
Externí odkaz:
http://arxiv.org/abs/2410.23871
Autor:
Kabgani, Alireza, Ahookhosh, Masoud
This paper introduces an inexact two-level smoothing optimization framework (ItsOPT)} for finding first-order critical points of nonsmooth and nonconvex functions. The framework involves two levels of methodologies: at the upper level, a first- or se
Externí odkaz:
http://arxiv.org/abs/2410.19928
In this paper, for the first time in the literature, we study the stability of solutions of two classes of feasibility (i.e., split equality and split feasibility) problems by set-valued and variational analysis techniques. Our idea is to equivalentl
Externí odkaz:
http://arxiv.org/abs/2410.16856
Autor:
Mordukhovich, Boris S., Nguyen, Oanh
The paper is devoted to developing subdifferential theory for set-valued mappings taking values in ordered infinite-dimensional spaces. This study is motivated by applications to problems of vector and set optimization with various constraints in inf
Externí odkaz:
http://arxiv.org/abs/2410.11362