We address the problem of deriving optimal inequalities for P(X E S), for a multivariate random variable X that has a given collection of moments, and S is an arbitrary set. Our goal in this paper is twofold: First, to present the beautiful interplay of probability and optimization related to moment inequalities, from a modern, optimization based, perspective. Second, to understand the complexity of deriving tight moment inequalities, search for efficient algorithms in a general framework, and, when possible, derive simple closed-form bounds. For the univariate case we provide an optimal inequality for P(X E S) for a single random variable X, when its first k moments are known, as a solution of a semidefinite optimization problem in k + 1 d...
The multivariate discrete moment problem (MDMP) is to find the minimum and/or maximum of the expecte...
The discrete moment problem (DMP) has been formulated as a methodology to find the minimum and/or ma...
Current results in bounding the expectation of convex functions in a single and in multiple dimensio...
Title from cover. "June 1999."Includes bibliographical references (leaves 47-52).Partially supported...
Abstract. We propose a semidefinite optimization approach to the problem of deriving tight moment in...
Title from cover. "May, 1998."Includes bibliographical references (p. 39-40).Supported in part by an...
Consider the problem of computing the optimal lower and upper bound for the expected value E[?(X)], ...
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics; and, (Ph.D.)--Massachus...
A sharp lower bound on the probability of a set defined by quadratic inequalities, given the first t...
AbstractA unified approach is used to rediscover a class of moment inequalities. In particular, comp...
The research is concerned with extremal tasks of a final generalized problem of moments on convex cl...
AbstractMoment problems, with finite, preassigned support, regarding the probability distribution, a...
AbstractMoment problems, with finite, preassigned support, regarding the probability distribution, a...
Abstract. We consider probabilistically constrained problems, in which the multivariate random varia...
This report constitutes the Doctoral Dissertation for Munevver Mine Subasi and consists of three top...
The multivariate discrete moment problem (MDMP) is to find the minimum and/or maximum of the expecte...
The discrete moment problem (DMP) has been formulated as a methodology to find the minimum and/or ma...
Current results in bounding the expectation of convex functions in a single and in multiple dimensio...
Title from cover. "June 1999."Includes bibliographical references (leaves 47-52).Partially supported...
Abstract. We propose a semidefinite optimization approach to the problem of deriving tight moment in...
Title from cover. "May, 1998."Includes bibliographical references (p. 39-40).Supported in part by an...
Consider the problem of computing the optimal lower and upper bound for the expected value E[?(X)], ...
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics; and, (Ph.D.)--Massachus...
A sharp lower bound on the probability of a set defined by quadratic inequalities, given the first t...
AbstractA unified approach is used to rediscover a class of moment inequalities. In particular, comp...
The research is concerned with extremal tasks of a final generalized problem of moments on convex cl...
AbstractMoment problems, with finite, preassigned support, regarding the probability distribution, a...
AbstractMoment problems, with finite, preassigned support, regarding the probability distribution, a...
Abstract. We consider probabilistically constrained problems, in which the multivariate random varia...
This report constitutes the Doctoral Dissertation for Munevver Mine Subasi and consists of three top...
The multivariate discrete moment problem (MDMP) is to find the minimum and/or maximum of the expecte...
The discrete moment problem (DMP) has been formulated as a methodology to find the minimum and/or ma...
Current results in bounding the expectation of convex functions in a single and in multiple dimensio...