Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications
Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.
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affine mapping algorithm arithmetic assume canonical barrier central path closed convex coefficients complexity conic problem Consequently constraints convex function convex hull convex optimization convex set corresponding CQr set Data(p design variables diagonal diagram direct product dual problem eigenvalues ellipsoid containing ellipsoid method entries epigraph equations equivalent exactly example Exercise exists fact Farkas lemma feasible set finite function given graph infeasible interior point methods intersection linear inequalities LMIs load lower bound LP program Lyapunov minimize n x n nodes nonempty nonnegative Note optimal solution optimal value optimization problem optimization programs orthogonal parameter path-following method positive definite positive semidefinite primal primal-dual pair Prš proof Proposition Prove quadratic form quadratic inequality result S-lemma satisfies Schur complement semidefinite program solvable solve symmetric matrix trigonometric polynomial truss Tschebyshev TTD problem verify