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Convex programming for disjunctive convex optimization
Mathematical Programming, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
João Soares, Sebastián Ceria
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Mathematics of Operations Research, 1998
We study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set U, yet the constraints must hold for all possible values of the data from U. The ensuing optimization problem is called robust optimization. In this paper we lay the foundation of robust convex optimization.
NemirovskiA., Ben-TalA.
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We study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set U, yet the constraints must hold for all possible values of the data from U. The ensuing optimization problem is called robust optimization. In this paper we lay the foundation of robust convex optimization.
NemirovskiA., Ben-TalA.
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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
2001In 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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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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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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Duality in Convex Optimization
2011A 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
2018Convex 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 +1 more
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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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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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Convexity, Optimization, and Inequalities
2010Convexity is one of the key concepts of mathematical analysis and has interesting consequences for optimization theory, statistical estimation, inequalities, and applied probability. Despite this fact, students seldom see convexity presented in a coherent fashion. It always seems to take a backseat to more pressing topics.
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