Fréchet subdifferential calculus and optimality conditions in nondifferentiable programming
From MaRDI portal
Publication:3426240
DOI10.1080/02331930600816395zbMath1121.49017OpenAlexW2057578212MaRDI QIDQ3426240
Nguyen Mau Nam, Boris S. Mordukhovich, Nguyen Dong Yen
Publication date: 8 March 2007
Published in: Optimization (Search for Journal in Brave)
Full work available at URL: https://digitalcommons.wayne.edu/math_reports/29
Related Items (75)
Calculus rules of generalized \(\epsilon\)-subdifferential for vector valued mappings and applications ⋮ Generalized penalization and maximization of vectorial nonsmooth functions ⋮ Optimality and duality in nonsmooth composite vector optimization and applications ⋮ Optimality conditions for robust nonsmooth multiobjective optimization problems in asplund spaces ⋮ Subgradients of the value function in a parametric convex optimal control problem ⋮ Some results concerning chain rules for Dini-Hadamard constructions ⋮ Weak sharp efficiency in multiobjective optimization ⋮ Optimality conditions of quasi $(\alpha,\varepsilon)$-solutions and approximate mixed type duality for DC composite optimization problems ⋮ Relative Pareto minimizers for multiobjective problems: Existence and optimality conditions ⋮ Approximate solutions in nonsmooth and nonconvex cone constrained vector optimization ⋮ Calculus of tangent sets and derivatives of set-valued maps under metric subregularity conditions ⋮ Zeroth-Order Regularized Optimization (ZORO): Approximately Sparse Gradients and Adaptive Sampling ⋮ On the problem of minimizing a difference of polyhedral convex functions under linear constraints ⋮ Enhanced Karush-Kuhn-Tucker condition and weaker constraint qualifications ⋮ NECESSARY OPTIMALITY CONDITIONS FOR SUPER MINIMIZERS IN STRUCTURAL PROBLEMS OF MULTIOBJECTIVE OPTIMIZATION ⋮ On the rotational invariant \(L_1\)-norm PCA ⋮ Second-order subdifferentials and convexity of real-valued functions ⋮ A proximal algorithm with backtracked extrapolation for a class of structured fractional programming ⋮ Strong Fermat rules for constrained set-valued optimization problems on Banach spaces ⋮ New Bregman proximal type algoritms for solving DC optimization problems ⋮ Fréchet subdifferential calculus for interval-valued functions and its applications in nonsmooth interval optimization ⋮ Variational analysis of marginal functions with applications to bilevel programming ⋮ Inertial Proximal Block Coordinate Method for a Class of Nonsmooth Sum-of-Ratios Optimization Problems ⋮ Fuzzy multiplier, sum and intersection rules in non-Lipschitzian settings: decoupling approach revisited ⋮ Robust optimality and duality for composite uncertain multiobjective optimization in Asplund spaces with its applications ⋮ Approximate solutions for robust multiobjective optimization programming in Asplund spaces ⋮ A note on an approximate mean value theorem for Fréchet subgradients ⋮ Convergence analysis of a proximal point algorithm for minimizing differences of functions ⋮ Unnamed Item ⋮ Complete characterizations of local weak sharp minima with applications to semi-infinite optimization and complementarity ⋮ Isolated and proper efficiencies in semi-infinite vector optimization problems ⋮ Optimality conditions for weak and firm efficiency in set-valued optimization ⋮ A new penalization tool in scalar and vector optimizations ⋮ Second-order characterizations of quasiconvexity and pseudoconvexity for differentiable functions with Lipschitzian derivatives ⋮ Two-level value function approach to non-smooth optimistic and pessimistic bilevel programs ⋮ Optimality conditions and duality in nonsmooth multiobjective optimization problems ⋮ New Applications of Variational Analysis to Optimization and Control ⋮ Approximate versions of proximal iteratively reweighted algorithms including an extended IP-ICMM for signal and image processing problems ⋮ Second-order optimality conditions for efficiency in \(C^{1,1}\)-smooth quasiconvex multiobjective programming problem ⋮ Alternating direction method of multipliers for a class of nonconvex bilinear optimization: convergence analysis and applications ⋮ Subgradients of marginal functions in parametric mathematical programming ⋮ Nonsmooth semi-infinite multiobjective optimization problems ⋮ Remarks on strict efficiency in scalar and vector optimization ⋮ On the Dini-Hadamard subdifferential of the difference of two functions ⋮ New necessary optimality conditions in optimistic bilevel programming ⋮ Optimality conditions for mixed discrete bilevel optimization problems ⋮ Subgradients of the value function to a parametric optimal control problem ⋮ Strong duality and optimality conditions for generalized equilibrium problems ⋮ Necessary conditions for super minimizers in constrained multiobjective optimization ⋮ On the robust PCA and Weiszfeld's algorithm ⋮ Nonconvex weak sharp minima on Riemannian manifolds ⋮ Optimality and duality in nonsmooth conic vector optimization ⋮ On the Dini-Hadamard-like coderivative of the difference of two single-valued mappings ⋮ Necessary optimality conditions for weak sharp minima in set-valued optimization ⋮ Sufficient conditions for error bounds of difference functions and applications ⋮ Subgradients of value functions in parametric dynamic programming ⋮ Second-order characterizations of \(\mathcal{C}^1\)-smooth robustly quasiconvex functions ⋮ Bilevel programming problems with simple convex lower level ⋮ Optimality conditions and total dualities for conic programming involving composite function ⋮ Mordukhovich subgradients of the value function to a parametric discrete optimal control problem ⋮ Optimality conditions for minimizing the difference of nonconvex vector-valued mappings ⋮ Coderivative necessary optimality conditions for sharp and robust efficiencies in vector optimization with variable ordering structure ⋮ On Algorithms for Difference of Monotone Operators ⋮ On Algorithms for Difference of Monotone Operators ⋮ Differential stability of discrete optimal control problems with mixed contraints ⋮ A hybrid Bregman alternating direction method of multipliers for the linearly constrained difference-of-convex problems ⋮ Min-sup-type zero duality gap properties for DC composite optimization problem ⋮ Strict directional solutions in vectorial problems: necessary optimality conditions ⋮ Optimality conditions and duality for DC programming in locally convex spaces ⋮ Optimality results for a specific fractional problem ⋮ Sensitivity analysis in parametric multiobjective discrete-time control via Fréchet subdifferential calculus of the frontier map ⋮ Subgradients of the Value Function via Multiplier Sets of Parametric Convex Discrete Optimal Control Problems ⋮ Bilevel Optimization and Variational Analysis ⋮ Extrapolated Proximal Subgradient Algorithms for Nonconvex and Nonsmooth Fractional Programs ⋮ Calmness and calculus: two basic patterns
Cites Work
This page was built for publication: Fréchet subdifferential calculus and optimality conditions in nondifferentiable programming
