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One of the main results in the theory is that the solution is provided by the linear–quadratic regulator (LQR), a feedback controller whose equations are given below. LQR controllers possess inherent robustness with guaranteed gain and phase margin, [1] and they also are part of the solution to the LQG (linear–quadratic–Gaussian) problem.
Design optimization applies the methods of mathematical optimization to design problem formulations and it is sometimes used interchangeably with the term engineering optimization. When the objective function f is a vector rather than a scalar , the problem becomes a multi-objective optimization one.
Random optimization (RO) is a family of numerical optimization methods that do not require the gradient of the optimization problem and RO can hence be used on functions that are not continuous or differentiable. Such optimization methods are also known as direct-search, derivative-free, or black-box methods.
In classical mechanics, the Udwadia–Kalaba formulation is a method for deriving the equations of motion of a constrained mechanical system. [1] [2] The method was first described by Anatolii Fedorovich Vereshchagin [3] [4] for the particular case of robotic arms, and later generalized to all mechanical systems by Firdaus E. Udwadia and Robert E. Kalaba in 1992. [5]
Quantum optimization algorithms are quantum algorithms that are used to solve optimization problems. [1] Mathematical optimization deals with finding the best solution to a problem (according to some criteria) from a set of possible solutions. Mostly, the optimization problem is formulated as a minimization problem, where one tries to minimize ...
Strong optimization problem (SOPT): given a vector c in R n, find a vector y in K such that c T y ≥ c T x for all x in K, or assert that K is empty. Strong violation problem (SVIOL) : given a vector c in R n and a number t , decide whether c T x ≤ t for all x in K , or find y in K such that c T y > t .
Mathematical optimization is the theory and computation of extrema or stationary points of functions. Optimization, optimisation, or optimality may also refer to: Engineering optimization; Feedback-directed optimisation, in computing; Optimality model in biology; Optimality theory, in linguistics; Optimization (role-playing games), a gaming ...
The FICO Xpress optimizer is a commercial optimization solver for linear programming (LP), mixed integer linear programming (MILP), convex quadratic programming (QP), convex quadratically constrained quadratic programming (QCQP), second-order cone programming (SOCP) and their mixed integer counterparts. [2]