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

to solve constrained minimization problems in optimization theory; see Lagrange multiplier Lagrangian relaxation, the method of approximating a difficult...

mathematical optimization, Lagrangian relaxation is a relaxation method which approximates a difficult problem of constrained optimization by a simpler...

solution corresponding to the original constrained optimization is always a saddle point of the Lagrangian function, which can be identified among the stationary...

generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from...

In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives...

In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least...

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently...

In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function...

Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the...

Bayesian optimization is a sequential design strategy for global optimization of black-box functions, that does not assume any functional forms. It is...

numerous optimization tasks involving some sort of graph, e.g., vehicle routing and internet routing. As an example, ant colony optimization is a class...

of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate...

an optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function. An optimization problem...

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

Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization, some or all of the...

Topological optimization techniques can then help work around the limitations of pure shape optimization. Mathematically, shape optimization can be posed...

D.; Price, C. J. (2002). "Positive Bases in Numerical Optimization". Computational Optimization and Applications. 21 (2): 169–176. doi:10.1023/A:1013760716801...

An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers...

sub-problems. In the optimization literature this relationship is called the Bellman equation. In terms of mathematical optimization, dynamic programming...

allows non-integer rational solutions. A Lagrangian relaxation of a complicated problem in combinatorial optimization penalizes violations of some constraints...

In physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, Hamiltonian...

understood as an instantaneous increment of the Lagrangian expression of the problem that is to be optimized over a certain time period. Inspired by—but distinct...

Limited-memory BFGS (L-BFGS or LM-BFGS) is an optimization algorithm in the family of quasi-Newton methods that approximates the Broyden–Fletcher–Goldfarb–Shanno...

programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject...

solving linear and nonlinear mathematical optimization problems. MINOS (Modular In-core Nonlinear Optimization System) may be used for linear programming...

necessarily convex. SQP methods solve a sequence of optimization subproblems, each of which optimizes a quadratic model of the objective subject to a linearization...

In numerical analysis, hill climbing is a mathematical optimization technique which belongs to the family of local search. It is an iterative algorithm...

In mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective...

algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on...