Convex optimization trust region

  • What is the difference between gradient descent and trust region?

    Gradient descent is a line search.
    We determine the descending direction first and then take a step towards that direction.
    In the trust region, we determine the maximum step size that we want to explore and then we locate the optimal point within this trust region..

  • What is the difference between line search and trust region?

    Line search method is based on searching a new iterative point along a descent direction at each iteration and trust region method is based on finding a new iterative point within a ball centered at the current iterate..

  • What is the Newton's method with a trust region?

    Description.
    Newton's method with a trust region is designed to take advantage of the second-order information in a function's Hessian, but with more stability that Newton's method when functions are not globally well-approximated by a quadratic..

  • What is trust region in optimization?

    In mathematical optimization, a trust region is the subset of the region of the objective function that is approximated using a model function (often a quadratic)..

  • What is trust region policy optimization?

    Trust Region Policy Optimization, or TRPO, is a policy gradient method in reinforcement learning that avoids parameter updates that change the policy too much with a KL divergence constraint on the size of the policy update at each iteration..

  • Gradient descent is a line search.
    We determine the descending direction first and then take a step towards that direction.
    In the trust region, we determine the maximum step size that we want to explore and then we locate the optimal point within this trust region.
  • Line search method is based on searching a new iterative point along a descent direction at each iteration and trust region method is based on finding a new iterative point within a ball centered at the current iterate.
  • The global convergence says the trust region method always converges to a stationary point.
    This is the same as the line search methods (under similar conditions).
    For local convergence, we consider the case that Bk = ∇2f(xk), we know that the model now is a second order approximation to the objection function locally.
In mathematical optimization, a trust region is the subset of the region of the objective function that is approximated using a model function (often a 

Example

Conceptually, in the Levenberg–Marquardt algorithm, the objective function is iteratively approximated by a quadratic surface, then using …

External links

• Kranf site: Trust Region Algorithms• Trust-region methods

Does the trust-region Newton method apply to polyhedral feasible sets?

For comparison, the trust-region Newton method proposed in [ 23] applies only to polyhedral feasible sets and employs a projected truncated conjugate gradient (CG) algorithm, accounting for the inactive constraints, to approximately solve the trust-region subproblem

What is a trust-region subproblem solver for convex-constrained optimization problems?

We described a trust-region subproblem solver for convex-constrained optimization problems based on the SPG method

Our algorithm is simple to implement, compared with other convex-constrained trust-region algorithms

In addition, our approach is completely matrix free, enabling the solution of enormous problems

What is trust region method?

Autor: Chun-Yu Chou, Ting-Guang Yeh, Yun-Chung Pan, Chen-Hua Wang (CHEME 6800, Fall 2021) Trust region method is a numerical optimization method that is employed to solve non-linear programming (NLP) problems

In mathematical optimization, a trust region is the subset of the region of the objective function that is approximated using a model function.
If an adequate model of the objective function is found within the trust region, then the region is expanded; conversely, if the approximation is poor, then the region is contracted.

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