17 articles
Augmented Lagrangian method
The augmented Lagrangian method (ALM), originally called the method of multipliers, is a constrained optimization algorithm combining the Lagrangian with a quadratic penalty term and Lagrange multiplier estimates.
Basis pursuit
Basis pursuit is an optimization principle for sparse signal recovery, selecting the smallest ℓ1-norm solution to Ax = b, solvable as a linear program; Chen, Donoho, and Saunders introduced it in 1998.
Chance-constrained optimization
Chance-constrained optimization is an approach to decision making under uncertainty in which a constraint on random data must hold with at least a specified probability, first formulated by Charnes, Cooper, and Symonds in 1958.
Ellipsoid method
The ellipsoid method is an iterative algorithm for convex optimization that shrinks enclosing ellipsoids, used by Khachiyan in 1979 to prove linear programming solvable in polynomial time.
Fractional programming
Fractional programming is the branch of optimization that maximizes or minimizes ratios of functions, such as signal-to-noise ratio or energy efficiency, solved with Dinkelbach's transform and the quadratic transform.
Fuzzy linear programming
Fuzzy linear programming (FLP) treats the parameters, constraints, or objectives of linear programming models as fuzzy, so constraints and goals are satisfied to varying degrees.
Geometric programming
Geometric programming is an optimization method with posynomial objectives and constraints that becomes convex after a logarithmic change of variables, so interior-point algorithms find the global optimum efficiently.
Golden-section search
Golden-section search is a derivative-free method for finding the minimum of a unimodal function on an interval, shrinking it by the golden ratio each iteration using only function evaluations.
Interval optimization
Interval optimization is a family of numerical methods that represent uncertain quantities as intervals and use interval arithmetic to compute guaranteed, rigorously correct bounds on a function's global optimum.
Knitro
Knitro, also sold as Artelys Knitro, is a commercial library for nonlinear optimization that originated at Northwestern University in the 1990s under Jorge Nocedal and is now developed by Artelys.
Minimax optimization
Minimax optimization seeks a saddle point where one player minimizes a shared objective and an adversary maximizes it, the formal language of GANs and robust learning.
Mixed-integer nonlinear programming
Mixed-integer nonlinear programming (MINLP), or integer nonlinear programming, is an optimization method for nonlinear problems in which some variables are restricted to integer values, making it NP-hard.
Proximal point algorithm
The proximal point algorithm, or proximal point method, is an iterative optimization method that repeatedly minimizes a convex objective plus a quadratic penalty centered at the current iterate.
Scenario reduction
Scenario reduction is a computational method in stochastic optimization that replaces a large sample of scenarios with a smaller subset of the original scenarios carrying adjusted probabilities.
SNOPT
SNOPT (Sparse Nonlinear OPTimizer) is a software package for large-scale linear and nonlinear constrained optimization, developed by Philip Gill, Walter Murray, and Michael Saunders and widely used for aerospace trajectory optimization.
Sparse optimization
Sparse optimization is a class of optimization methods that seek solutions with few nonzero variables, using sparsity-inducing penalties or constraints such as the lasso and basis pursuit.
Unconstrained binary optimization
Unconstrained binary optimization (UBO) is the class of problems optimizing an objective over binary variables with no explicit constraints, its standard form being the quadratic unconstrained binary optimization (QUBO) model.