A differentiable homotopy approach for solving polynomial optimization problems and noncooperative games

DOI10.1016/0898-1221(91)90168-4zbMath0721.90071OpenAlexW2028064704MaRDI QIDQ2641225

L. A. Kinard, Michael M. Kostreva

Publication date: 1991

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(91)90168-4

zbMATH Keywords

polynomial systemdifferentiable homotopyabsolute error comparisons

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Noncooperative games (91A10) Nonlinear programming (90C30) Numerical computation of solutions to systems of equations (65H10) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Computational methods for problems pertaining to operations research and mathematical programming (90-08)

Related Items (7)

Homotopy methods to compute equilibria in game theory ⋮ Multiple-objective approximation of feasible but unsolvable linear complementarity problems ⋮ A mixed 0-1 linear programming approach to the computation of all pure-strategy Nash equilibria of a finite \(n\)-person game in normal form ⋮ Semidefinite programming for min-max problems and games ⋮ Polynomial programming using multi-homogeneous polynomial continuation ⋮ Multiple-objective programming with polynomial objectives and constraints ⋮ A globally convergent algorithm to compute all Nash equilibria for \(n\)-person games

Uses Software

• HOMPACK

Cites Work

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• Non-convexity in noncooperative game theory
• Test examples for nonlinear programming codes
• Sandwich method for finding fixed points
• Algorithm 652
• Computation of all solutions to a system of polynomial equations
• Finding All Solutions to a System of Polynomial Equations
• Equilibrium Points of Bimatrix Games
• The Approximation of Fixed Points of a Continuous Mapping
• SIMPLICIAL APPROXIMATION OF FIXED POINTS
• The Solution of Nonlinear Systems of Equations by A-Stable Integration Techniques
• Homotopies for computation of fixed points on unbounded regions

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