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

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...

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

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

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

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

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

In physics, Lagrangian mechanics is an alternate formulation of classical mechanics founded on the d'Alembert principle of virtual work. It was introduced...

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

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

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

Rate-distortion optimization (RDO) is a method of improving video quality in video compression. The name refers to the optimization of the amount of distortion...

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

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

predictive analytics. The key motivation behind multi-task optimization is that if optimization tasks are related to each other in terms of their optimal...

widely used for constructing the dual problem in optimization theory, thus generalizing Lagrangian duality. Let X {\displaystyle X} be a real topological...

{\displaystyle g_{i}(x)\geqslant 0,i=1,\ldots ,r} . Global optimization is distinguished from local optimization by its focus on finding the minimum or maximum over...

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

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

Sollin are greedy algorithms that can solve this optimization problem. The heuristic method In optimization problems, heuristic algorithms find solutions...

design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic...

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

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

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

In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local...

stochastic optimization, so that the solution found is dependent on the set of random variables generated. In combinatorial optimization, there are many...

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

Lemaréchal, Claude (2001). "Lagrangian relaxation". In Michael Jünger and Denis Naddef (ed.). Computational combinatorial optimization: Papers from the Spring...