Second order optimality conditions for the \(L_ 1\)-minimization problem

DOI10.1007/BF01442198zbMath0566.49013OpenAlexW2998406152MaRDI QIDQ1059265

Jochem Zowe, Aharon Ben-Tal

Publication date: 1985

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01442198

zbMATH Keywords

unconstrained minimizationdirectional derivativeSecond order necessary and second order sufficient conditions

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Fréchet and Gateaux differentiability in optimization (49J50) Programming in abstract spaces (90C48) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20) Derivatives of functions in infinite-dimensional spaces (46G05) Optimality conditions for problems in abstract spaces (49K27)

Related Items (7)

Linear-quadratic control problems withL¹-control cost ⋮ Regularization and discretization error estimates for optimal control of ODEs with group sparsity ⋮ On constrained optimization problems with nonsmooth cost functionals ⋮ Second-order necessary optimality conditions for optimization problems involving set-valued maps ⋮ Necessary quadratic conditions of extremum for discontinuous controls in optimal control problems with mixed constraints ⋮ Sufficient quadratic conditions of extremum for discontinuous controls in optimal control problems with mixed constraints ⋮ Metric regularity, tangent sets, and second-order optimality conditions

Cites Work

• Unnamed Item
• Technical note: Directional derivatives in nonsmooth optimization
• Nonlinear \(L_1\) approximation of smooth functions
• Necessary and sufficient optimality conditions for a class of nonsmooth minimization problems
• A unified theory of first and second order conditions for extremum problems in topological vector spaces

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