Subgradient methods are convex optimization methods which use subderivatives. Originally developed by Naum Z. Shor and others in the 1960s and 1970s,...

functions. Cutting-plane methods Ellipsoid method Subgradient method Dual subgradients and the drift-plus-penalty method Subgradient methods can be implemented...

extrapolation Root-finding algorithm Secant method Steffensen's method Subgradient method "Chapter 2. Seki Takakazu". Japanese Mathematics in the Edo Period...

In mathematics, subderivatives (or subgradient) generalizes the derivative to convex functions which are not necessarily differentiable. The set of subderivatives...

and bundle methods. They are popularly used for non-differentiable convex minimization, where a convex objective function and its subgradient can be evaluated...

method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of an iterative method or a method of...

Interior-point methods (also referred to as barrier methods or IPMs) are algorithms for solving linear and non-linear convex optimization problems. IPMs...

The Nelder–Mead method (also downhill simplex method, amoeba method, or polytope method) is a numerical method used to find the minimum or maximum of an...

"efficient" methods use "divergent-series" step size rules, which were first developed for classical subgradient methods. Classical subgradient methods using...

In optimization, a gradient method is an algorithm to solve problems of the form min x ∈ R n f ( x ) {\displaystyle \min _{x\in \mathbb {R} ^{n}}\;f(x)}...

methods used to define the prior/posterior distribution over the objective function. The most common two methods use Gaussian processes in a method called...

operations research, the Big M method is a method of solving linear programming problems using the simplex algorithm. The Big M method extends the simplex algorithm...

unconstrained case, often via the use of a penalty method. However, search steps taken by the unconstrained method may be unacceptable for the constrained problem...

In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming. The name of the algorithm...

In numerical analysis, a quasi-Newton method is an iterative numerical method used either to find zeroes or to find local maxima and minima of functions...

known for his method of generalized gradient descent with space dilation in the direction of the difference of two successive subgradients (the so-called...

Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for minimizing a differentiable multivariate...

problem class, it typically becomes the method of choice because it is faster than other optimization methods like dynamic programming. Examples of such...

The descent direction can be computed by various methods, such as gradient descent or quasi-Newton method. The step size can be determined either exactly...

Penalty methods are a certain class of algorithms for solving constrained optimization problems. A penalty method replaces a constrained optimization...

boundary of the interval, it will converge to that boundary point. The method operates by successively narrowing the range of values on the specified...

functions was motivated by their connection with primal-dual interior point methods. Consider the following constrained optimization problem: minimize f(x)...

Lagrangian methods are a certain class of algorithms for solving constrained optimization problems. They have similarities to penalty methods in that they...

case of cone programming and can be efficiently solved by interior point methods. All linear programs and (convex) quadratic programs can be expressed as...

algorithm is an iterative method for solving unconstrained nonlinear optimization problems. Like the related Davidon–Fletcher–Powell method, BFGS determines the...

have a "subgradient oracle": a routine that can compute a subgradient of f at any given point (if f is differentiable, then the only subgradient is the...

(that is: compute the value of f(x) and a subgradient f'(x)). Under these assumptions, the ellipsoid method is "R-polynomial". This means that there exists...

reasonable approximation. Trust-region methods are in some sense dual to line-search methods: trust-region methods first choose a step size (the size of...

Powell's method, strictly Powell's conjugate direction method, is an algorithm proposed by Michael J. D. Powell for finding a local minimum of a function...

known as the conditional gradient method, reduced gradient algorithm and the convex combination algorithm, the method was originally proposed by Marguerite...