Nonlinear optimization in finite dimensions. Morse theory, Chebyshev approximation, transversality, flows, parametric aspects

Hubertus Th. Jongen, Peter Jonker, Frank Twilt

Publication date: 15 November 2000

Published in: Nonconvex Optimization and Its Applications (Search for Journal in Brave)

zbMATH Keywords

Morse theory critical point theory transversality optimization problems gradient flows Chebyshev approximation Newton flows stability of critical points

Mathematics Subject Classification ID

Nonlinear programming (90C30) Sensitivity, stability, parametric optimization (90C31) Methods of quasi-Newton type (90C53) Methods of reduced gradient type (90C52)

Related Items

Critical point theory for sparse recovery, Sufficient optimality conditions hold for almost all nonlinear semidefinite programs, The cone condition and nonsmoothness in linear generalized Nash games, A new proof of the index formula for incomplete markets, On generalized semi-infinite optimization of genetic networks, Generic Property of the Partial Calmness Condition for Bilevel Programming Problems, Approximation and decomposition properties of some classes of locally d.c. functions, Semi-infinite programming, Bilevel optimization: on the structure of the feasible set, Topological approach to mathematical programs with switching constraints, On saddle points in nonconvex semi-infinite programming, Newton flows for elliptic functions. II: Structural stability: classification and representation, Maximization of homogeneous polynomials over the simplex and the sphere: structure, stability, and generic behavior, A function approximation approach for parametric optimization, A survey on OR and mathematical methods applied on gene-environment networks, Unnamed Item, Strongly Stable Stationary Points for a Class of Generalized Equations, Optimality conditions for mathematical programs with orthogonality type constraints, Mathematical programs with vanishing constraints: critical point theory, Generic Properties for Semialgebraic Programs, Optimal sensitivity based on IPOPT, Genericity Results in Linear Conic Programming—A Tour d’Horizon, Newton flows for elliptic functions I, On intrinsic complexity of Nash equilibrium problems and bilevel optimization, On the qualitative approximation of Lipschitzian functions., Cooperative games under bubbly uncertainty, MPCC: on necessary conditions for the strong stability of C-stationary points, Strongly stable C-stationary points for mathematical programs with complementarity constraints, On the closure of the feasible set in generalized semi-infinite programming, Generalized semi-infinite programming: The symmetric reduction ansatz, Full symmetry implementation in condensed matter and molecular physics-modified group projector technique, Generalized semi-infinite programming: On generic local minimizers, On topological properties of min-max functions, Newton flows for elliptic functions III \& IV. Newton flows for elliptic functions III \& IV, pseudo Newton graphs: bifurcation and creation of flows, On absorbing cycles in min-max digraphs, On numerical optimization theory of infinite kernel learning, Global optimization: local minima and transition points, A geometric representation of the Morse fan, Convergent upper bounds in global minimization with nonlinear equality constraints, On the calculation of a feasible point of a nonconvex set: pathfollowing with jumps, Analytic approximation and differentiability of joint chance constraints, The structured jet transversality theorem†, Optimization of gene-environment networks in the presence of errors and uncertainty with Chebychev approximation, Generalized desirability functions: a structural and topological analysis of desirability functions, MPCC: strong stability of \(m\)-stationary points, Critical points index for vector functions and vector optimization, Constrained optimization: Projected gradient flows, On optimization, dynamics and uncertainty: A tutorial for gene-environment networks, Unnamed Item, MIN-MAX SOLUTIONS FOR PARAMETRIC CONTINUOUS STATIC GAME UNDER ROUGHNESS (PARAMETERS IN THE COST FUNCTION AND FEASIBLE REGION IS A ROUGH SET), Unnamed Item, Genericity Analysis of Multi-Leader-Disjoint-Followers Game, Deformations in the general position of the optimal functions on oriented surfaces with boundary, On nondegenerate M-stationary points for sparsity constrained nonlinear optimization