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SIAM Journal on Optimization, 2010
Random convex programs (RCPs) are convex optimization problems subject to a finite number $N$ of random constraints. The optimal objective value $J^*$ of an RCP is thus a random variable. We study the probability with which $J^*$ is no longer optimal if a further random constraint is added to the problem (violation probability, $V^*$).
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Random convex programs (RCPs) are convex optimization problems subject to a finite number $N$ of random constraints. The optimal objective value $J^*$ of an RCP is thus a random variable. We study the probability with which $J^*$ is no longer optimal if a further random constraint is added to the problem (violation probability, $V^*$).
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Preliminaries: Convex Analysis and Convex Programming
2001In this chapter, we give some definitions and results connected with convex analysis, convex programming, and Lagrangian duality. In Part Two, these concepts and results are utilized in developing suitable optimality conditions and numerical methods for solving some convex problems.
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2001
Convex programming studies problems of the form (CP) where the objective function f: Rn → R and the constraints fi: Rn → R, i * P are “convex functions”. “Convexity” is a magic word in the world of optimization, because it allows the results for local optima to be extended to global optima.
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Convex programming studies problems of the form (CP) where the objective function f: Rn → R and the constraints fi: Rn → R, i * P are “convex functions”. “Convexity” is a magic word in the world of optimization, because it allows the results for local optima to be extended to global optima.
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2001
As it was pointed out in Chapter Two, if f j (x j ) are strictly convex and g ij (x j ) are convex for i= 1,..., m and j ∉ L, the standard simplex method, discarding the restricted basis entry rule, is applicable to the approximating linear program (LASP) (2.17) – (2.21).
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As it was pointed out in Chapter Two, if f j (x j ) are strictly convex and g ij (x j ) are convex for i= 1,..., m and j ∉ L, the standard simplex method, discarding the restricted basis entry rule, is applicable to the approximating linear program (LASP) (2.17) – (2.21).
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2001
The theory of convex models can be used to study a large class of non-linear programs called “partly convex programs” (abbreviation: PCP).
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The theory of convex models can be used to study a large class of non-linear programs called “partly convex programs” (abbreviation: PCP).
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