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Solving Nonconvex Optimal Control Problems by Convex Optimization [PDF]

Journal of Guidance, Control, and Dynamics, 2013
Motivated by aerospace applications, this paper presents a methodology to use second-order cone programming to solve nonconvex optimal control problems. The nonconvexity arises from the presence of concave state inequality constraints and nonlinear terminal equality constraints.
Xinfu Liu, Ping Lu
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Convex Optimization With Convex Constraints

2001
In this chapter we want to solve the problem minf(x) | x ∈ C, where f is a convex function on ℝ n , and C is a convex, nonempty subset of ℝ n . A point x* ∈ C is a global solution, or more simply a solution to this problem, or a minimizer of f on C, if f(x*) ≤ f(x), ∀x ∈ C. We say that x* is a local solution to this problem if there exists a relatively
Cuong Le Van, Monique Florenzano
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Convexity and Optimization

2009
Optimization is a central theme of applied mathematics that involves minimizing or maximizing various quantities. This is an important application of the derivative tests in calculus. In addition to the first and second derivative tests of one-variable calculus, there is the powerful technique of Lagrange multipliers in several variables.
Kenneth R. Davidson, Allan P. Donsig
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Convex programming for disjunctive convex optimization

Mathematical Programming, 1999
Given a finite number of closed convex sets whose algebraic representation is known, we study the problem of finding the minimum of a convex function on the closure of the convex hull of the union of those sets. We derive an algebraic characterization of the feasible region in a higher-dimensional space and propose a solution procedure akin to the ...
João Soares, Sebastián Ceria
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Duality in Convex Optimization

2011
A convex optimization problem can be paired with a dual problem involving the conjugates of the functions appearing in its (primal) formulation. In this chapter, we study the interplay between primal and dual problems in the context of Fenchel–Rockafellar duality and, more generally, for bivariate functions.
Heinz H. Bauschke, Patrick L. Combettes
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Duality and Convex Optimization

2018
Convex optimization is one of the main applications of the theory of convexity and Legendre–Fenchel duality is a basic tool, making more flexible the approach of many concrete problems. The diet problem, the transportation problem, and the optimal assignment problem are among the many problems that during the Second World War and immediately after led ...
Constantin P. Niculescu, Lars-Erik Persson   +1 more
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A tutorial on convex optimization [PDF]

Proceedings of the 2004 American Control Conference, 2004
In recent years, convex optimization has become a computational tool of central importance in engineering, thanks to it's ability to solve very large, practical engineering problems reliably and efficiently. The goal of this tutorial is to give an overview of the basic concepts of convex sets, functions and convex optimization problems, so that the ...
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Smooth Convex Optimization

2004
In this chapter, we study the complexity of solving optimization problems formed by differentiable convex components. We start by establishing the main properties of such functions and deriving the lower complexity bounds, which are valid for all natural optimization methods.
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