Bifurcation problems in nonlinear parametric programming

DOI10.1007/BF02592952zbMath0639.90084OpenAlexW2047957544MaRDI QIDQ3780772

C. A. Tiahrt, Aubrey B. Poore

Publication date: 1987

Published in: Mathematical Programming (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02592952

zbMATH Keywords

singularityactive constraintsoptimal solutionnonlinear parametric programmingclosed system of nonlinear equationsnumerical continuation and bifurcation techniquessimple and multiple bifurcationunique persistence of a minimum

Mathematics Subject Classification ID

Nonlinear programming (90C30) Sensitivity, stability, parametric optimization (90C31) Numerical methods based on nonlinear programming (49M37)

Related Items

Regular and Critical States in Elastic Nonlinear Systems with Displacement Constraints, Global optimization of multi-parametric MILP problems, A direct application of higher‐order parametric programming techniques to structural optimization, Sequential quadratic programming methods for parametric nonlinear optimization, The exact solution of multiparametric quadratically constrained quadratic programming problems, On parametric nonlinear programming, Sensitivity analysis for variational inequalities and nonlinear complementarity problems, An algorithm constructing solutions for a family of linear semi-infinite problems., Bifurcations in piecewise-smooth steady-state problems: abstract study and application to plane contact problems with friction, Bifurcations in parametric nonlinear programming, A bifurcation analysis of the nonlinear parametric programming problem, Solution differentiability for variational inequalities

Uses Software

• AUTO
• PITCON

Cites Work

• One-parameter families of optimization problems: equality constraints
• Stability of parametrized families of gradient vector fields
• Introduction to sensitivity and stability analysis in nonlinear programming
• Theory of multiobjective optimization
• Singularities and groups in bifurcation theory. Volume I
• The Fritz John necessary optimality conditions in the presence of equality and inequality constraints
• A locally parameterized continuation process
• Continuous deformation of nonlinear programs
• Local Error Estimates for Parametrized Nonlinear Equations
• Structure of the first-order solution set for a class of nonlinear programs with parameters
• Critical sets in parametric optimization
• Solution Fields of Nonlinear Equations and Continuation Methods
• Strongly Regular Generalized Equations
• Stability Theory for Systems of Inequalities, Part II: Differentiable Nonlinear Systems
• Application of Degree Theory in Stability of the Complementarity Problem
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