Variational Problems and Applications

• Other Authors: Treanta, Savin (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel MDPI - Multidisciplinary Digital Publishing Institute 2023
• Subjects: Information technology industries; Computer science; Lagrange 1-form; second-order Lagrangian; normal weak robust optimal solution; modified objective function method; robust saddle-point; real analysis; Riemann integral; change of variable; constrained variational problem; well-posedness; multiple integral functional; gH-symmetrically derivative; optimality conditions; wolfe duality; symmetric pseudo-convexity; symmetric quasi-convexity; LR-χ-pre-invex interval-valued function; interval Riemann-Liouville fractional integral operator; Hermite-Hadamard inequality; Hermite-Hadamard Fejér inequality; Hermite-Hadamard inequalities; harmonical convex functions; interval-valued functions; fractional integrals; left and right preinvex interval-valued function; interval Riemann integral; Hermite-Hadamard type inequality; Hermite-Hadamard-Fejér type inequality; nonlinear function; constrained optimization; hybrid algorithm; global optima; line search; gradient method; meta-heuristics; simulated annealing algorithm; constraint handling; penalty function; evolutionary computation; numerical comparisons; metaheuristics; feature selection; classification; nonlocal modified Korteweg-de Vries equation; consistent tanh expansion method; parity-time symmetry; multi-time controlled Lagrangian of second-order; isoperimetric constraints; Euler-Lagrange equations; multiple integral; differential 1-form; curvilinear integral; variational inequalities; nonlinear programming; switching constraints; stationary conditions; interval-valued optimization; polynomial approximation; unbounded subsets; Markov moment problem; positive operators; solution; existence; uniqueness; sums of squares; Banach lattices; BVP nonlinear problems; variational methods; estimating nonlinearities; Green function; n/a
• Online Access: DOAB: download the publication; DOAB: description of the publication

The current reprint presents studies of uncertain variational problems. It aims to develop the research in this field by formulating and demonstrating some characterization results of well-posedness and robust efficient solutions in new classes of (multiobjective) variational (control) problems governed by multiple and/or path-independent curvilinear integral cost functionals and robust mixed and/or isoperimetric constraints involving first- and second-order partial differential equations.