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The "second-order cone" in SOCP arises from the constraints, which are equivalent to requiring the affine function (+, +) to lie in the second-order cone in +. [ 1 ] SOCPs can be solved by interior point methods [ 2 ] and in general, can be solved more efficiently than semidefinite programming (SDP) problems. [ 3 ]
GPOPS-II (pronounced "GPOPS 2") is a general-purpose MATLAB software for solving continuous optimal control problems using hp-adaptive Gaussian quadrature collocation and sparse nonlinear programming.
Many optimization problems can be equivalently formulated in this standard form. For example, the problem of maximizing a concave function can be re-formulated equivalently as the problem of minimizing the convex function . The problem of maximizing a concave function over a convex set is commonly called a convex optimization problem.
The artificial landscapes presented herein for single-objective optimization problems are taken from Bäck, [1] Haupt et al. [2] and from Rody Oldenhuis software. [3] Given the number of problems (55 in total), just a few are presented here. The test functions used to evaluate the algorithms for MOP were taken from Deb, [4] Binh et al. [5] and ...
[1] [2] It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering [3] to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. [4] [5]
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
The problem of finding the best ordering is an NP-complete problem and is thus intractable, so heuristic methods are used instead. The minimum degree algorithm is derived from a method first proposed by Markowitz in 1959 for non-symmetric linear programming problems, which is loosely described as follows.
The conjugate gradient method can also be used to solve unconstrained optimization problems such as energy minimization. It is commonly attributed to Magnus Hestenes and Eduard Stiefel, [1] [2] who programmed it on the Z4, [3] and extensively researched it. [4] [5] The biconjugate gradient method provides a generalization to non-symmetric matrices.