Gradient method

In optimization, gradient method is an algorithm to solve problems of the form

with the search directions defined by the gradient of the function at the current point. Examples of gradient method are the gradient descent and the conjugate gradient.

See also

Gradient descent method Conjugate gradient method Derivation of the conjugate gradient method Nonlinear conjugate gradient method Biconjugate gradient method Biconjugate gradient stabilized method References Elijah Polak (1997). Optimization : Algorithms and Consistent Approximations. Springer-Verlag. ISBN 0-387-94971-2.  Optimization: Algorithms, methods, and heuristics   Unconstrained nonlinear: Methods calling … … functions Golden section search Interpolation methods Line search Nelder–Mead method Successive parabolic interpolation … and gradients Convergence Trust region Wolfe conditions Quasi–Newton BFGS and L-BFGS DFP Symmetric rank-one (SR1) Other methods Gauss–Newton Gradient Levenberg–Marquardt Conjugate gradient Truncated Newton … and Hessians Newton's method   Constrained nonlinear General Barrier methods Penalty methods Differentiable Augmented Lagrangian methods Sequential quadratic programming Successive linear programming   Convex optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-Exchange Simplex algorithm of Dantzig Revised simplex algorithm Criss-cross algorithm Principal pivoting algorithm of Lemke   Combinatorial Paradigms Approximation algorithm Dynamic programming Greedy algorithm Integer programming Branch & bound or cut Graph algorithms Minimum spanning tree Bellman–Ford Borůvka Dijkstra Floyd–Warshall Johnson Kruskal Network flows Dinic Edmonds–Karp Ford–Fulkerson Push–relabel maximum flow   Metaheuristics Evolutionary algorithm Hill climbing Local search Simulated annealing Tabu search Categories Algorithms and methods Heuristics Software