Variational Problems and Applications

doi:10.3390/books978-3-0365-6588-0

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https://mdpi.com/books/pdfview/book/6750

Contributor(s)

Treanta, Savin (editor)

Language

English

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Abstract

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.

URI

https://directory.doabooks.org/handle/20.500.12854/98023

Keywords

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