Nonlinear Analysis and Optimization with Applications

• Other Authors: Du, Wei-Shih (Editor), Chu, Liang-Ju (Editor), He, Fei (Editor), Precup, Radu (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel MDPI - Multidisciplinary Digital Publishing Institute 2022
• Subjects: Research & information: general; Mathematics & science; best proximity point; fixed point; monotone mappings; relatively cyclic nonexpansive mappings; partially ordered Banach spaces; modified BBM equations; (3+1)-dimensional equations; white noise; Brownian motion; travelling wave solutions; wick-type stochastic; admissible spaces; hybrid contraction; interpolative contraction; b-metric spaces; simulation function; m-metric space; proximal αp-admissible; αp-admissible weak (F,φ)-proximal contraction; G-proximal graphic contraction; φ-best proximity point; Fourier data; reconstruction; multivariate approximation; piecewise smooth; projection methods; strong convergence; extragradient method; monotone mapping; variational inequalities; critical index; relaxation time; time-translation invariance breaking and restoration; market crash; COVID-19; Gompertz approximants; split common null point; resolvent; metric resolvent; split minimization problem; split equilibrium problem; Banach space; multiple-sets split feasibility problem; strictly pseudocontractive mappings; nonexpansive mappings; viscossity iterative scheme; fixed point problem; n-Banach space; cubic mappings; quartic mappings; the generalized Hyers-Ulam stability; maximal element; sizing-up function; μ-bounded quasi-ordered set; critical point; fuzzy mapping; Ekeland's variational principle; Caristi's fixed point theorem; Takahashi's nonconvex minimization theorem; essential distance
• Online Access: DOAB: download the publication; DOAB: description of the publication

Nonlinear analysis has wide and significant applications in many areas of mathematics, including functional analysis, variational analysis, nonlinear optimization, convex analysis, nonlinear ordinary and partial differential equations, dynamical system theory, mathematical economics, game theory, signal processing, control theory, data mining, and so forth. Optimization problems have been intensively investigated, and various feasible methods in analyzing convergence of algorithms have been developed over the last half century. In this Special Issue, we will focus on the connection between nonlinear analysis and optimization as well as their applications to integrate basic science into the real world.