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Convex optimization is a subfield of ... Theory and Examples, Second Edition (PDF ... Convex Optimization Book by Lieven Vandenberghe and Stephen P. Boyd
In 1994, Boyd and Laurent El Ghaoui, Eric Feron, and Ragu Balakrishnan authored the book Linear Matrix Inequalities in System & Control Theory. [15] Around 1999, he and Lieven Vandenberghe developed a PhD-level course and wrote the book Convex Optimization to introduce and apply convex optimization to other fields. [13]
Convex quadratically constrained quadratic programs can also be formulated as SOCPs by reformulating the objective function as a constraint. [4] Semidefinite programming subsumes SOCPs as the SOCP constraints can be written as linear matrix inequalities (LMI) and can be reformulated as an instance of semidefinite program. [ 4 ]
Proximal gradient methods are a generalized form of projection used to solve non-differentiable convex optimization problems. A comparison between the iterates of the projected gradient method (in red) and the Frank-Wolfe method (in green). Many interesting problems can be formulated as convex optimization problems of the form
The optimization of sequential experimentation is studied also in stochastic programming and in systems and control. Popular methods include stochastic approximation and other methods of stochastic optimization. Much of this research has been associated with the subdiscipline of system identification. [30]
Conic optimization is a subfield of convex optimization that studies problems consisting of minimizing a convex function over the intersection of an affine subspace and a convex cone. The class of conic optimization problems includes some of the most well known classes of convex optimization problems, namely linear and semidefinite programming .
Convex analysis includes not only the study of convex subsets of Euclidean spaces but also the study of convex functions on abstract spaces. Convex analysis is the branch of mathematics devoted to the study of properties of convex functions and convex sets , often with applications in convex minimization , a subdomain of optimization theory .
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