\(\alpha\)-concave functions and measures and their applications

DOI10.1007/BF01246517zbMath0875.90336MaRDI QIDQ1816039

Vladimir I. Norkin, N. V. Roenko

Publication date: 18 December 1996

Published in: Cybernetics and Systems Analysis (Search for Journal in Brave)

zbMATH Keywords

quasiconcave functionprobability optimization

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26)

Related Items (9)

Construction of confidence absorbing set for analysis of static stochastic systems ⋮ Modality for scenario analysis and maximum likelihood allocation ⋮ Augmented Lagrangian method for probabilistic optimization ⋮ Optimization of the quantile criterion for the convex loss function by a stochastic quasigradient algorithm ⋮ Regularization methods for optimization problems with probabilistic constraints ⋮ Sufficient conditions for quasiconcavity of the probability function ⋮ Construction of confidence absorbing sets using statistical methods ⋮ Convergence conditions for the observed mean method in stochastic programming ⋮ Convexity of chance constrained programming problems with respect to a new generalized concavity notion

Cites Work

• Über eine Klasse superadditiver Mengenfunktionale von Brunn-Minkowski- Lusternikschem Typus
• Brunn-Minkowski inequality and its aftermath
• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• On convexity of measures
• Contributions to the theory of stochastic programming
• Convex Analysis
• A Review of Quasi-Convex Functions
• On the Measure of Sum-Sets. (I) The Theorems of Brunn, Minkowski, and Lusternik
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