Modern homotopy methods in optimization
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Publication:908661
DOI10.1016/0045-7825(89)90053-4zbMath0693.65046OpenAlexW2039094757MaRDI QIDQ908661
Raphael T. Haftka, Layne T. Watson
Publication date: 1989
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: http://eprints.cs.vt.edu/archive/00000135/
algorithmsglobal convergencefinite elementsfinite differencescollocationunconstrained and constrained optimizationshootingBrouwer fixed point problemsengineering optimization problemspolynomial systems of equationsProbability-one homotopy methods
Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Numerical computation of solutions to systems of equations (65H10)
Related Items (26)
The method based on series solution for identifying an unknown source coefficient on the temperature field in the quasiperiodic media ⋮ The homotopy analysis method to solve the Burgers-Huxley equation ⋮ A study on the \(d\)-dimensional Schrödinger equation with a power-law nonlinearity ⋮ Non-uniqueness and symmetry of optimal topology of a shell for minimum compliance ⋮ Solving the inverse problem of identifying an unknown source term in a parabolic equation ⋮ An efficient algorithm for solving generalized pantograph equations with linear functional argument ⋮ A projected homotopy perturbation method for nonlinear inverse problems in Banach spaces ⋮ Hyperbolic smoothing and penalty techniques applied to molecular structure determination ⋮ Tutorial on Amortized Optimization ⋮ A homotopy alternating direction method of multipliers for linearly constrained separable convex optimization ⋮ Parameter identification in dynamic systems using the homotopy optimization approach ⋮ Shape-stress trade-off design of membrane structures for specified sequence of boundary shapes ⋮ Exploring collision-free path planning by using homotopy continuation methods ⋮ Solving the backward heat conduction problem by homotopy analysis method ⋮ The Trimmed Lasso: Sparse Recovery Guarantees and Practical Optimization by the Generalized Soft-Min Penalty ⋮ Numerical solutions of highly oscillatory integrals ⋮ A study on the PDEs with power-law nonlinearity ⋮ A series solution of the nonlinear Volterra and Fredholm integro-differential equations ⋮ A weighted algorithm based on the homotopy analysis method: application to inverse heat conduction problems ⋮ Black-box learning of multigrid parameters ⋮ Probability-one homotopy maps for mixed complementarity problems ⋮ Application of weighted homotopy analysis method to solve an inverse source problem for wave equation ⋮ Path-following proximal approach for solving ill-posed convex semi-infinite programming problems ⋮ A time continuation based fast approximate algorithm for compressed sensing related optimization ⋮ Probability-one homotopy algorithms for solving the coupled Lyapunov equations arising in reduced-order \(H^2/H^\infty\) modeling, estimation, and control ⋮ Probability-one homotopies in computational science
Uses Software
Cites Work
- CONKUB: A conversational path-follower for systems of nonlinear equations
- Tracing structural optima as a function of available resources by a homotopy method
- A globally convergent algorithm for computing fixed points of \(C^2\) maps
- A homotopy method applied to elastica problems
- Algorithm 652
- Numerical Linear Algebra Aspects of Globally Convergent Homotopy Methods
- The Expanded Lagrangian System for Constrained Optimization Problems
- Continuous Homotopies for the Linear Complementarity Problem
- Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations
- Computational experience with the Chow—Yorke algorithm
- Algorithm 555: Chow-Yorke Algorithm for Fixed Points or Zeros of C 2 Maps [C5]
- Optimal design by a homotopy method
- Equivalence of the Complementarity Problem to a System of Nonlinear Equations
- Finding Zeroes of Maps: Homotopy Methods That are Constructive With Probability One
- Solving the Nonlinear Complementarity Problem by a Homotopy Method
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