We study a deterministic linear-quadratic (LQ) control problem over an infinite horizon, and develop a general apprach to the problem based on semi-definite programming (SDP)and related duality analysis. This approach allows the control cost matrix R to be non-negative (semi-definite), a case...

We study stochastic linear--quadratic (LQ) optimal control problems over an infinite horizon, allowing the cost matrices to be indefinite. We develop a systematic approach based on semidefinite programming (SDP). A central issue is the stability of the feedback control; and we show this can be...

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In this work, we give a tight estimate of the rate of convergence for the Halpern-iteration for approximating a fixed point of a nonexpansive mapping in a Hilbert space. Specifically, using semidefinite programming and duality we prove that the norm of the residuals is upper bounded by the...

In this paper we study the properties of the analytic central path of asemidefinite programming problem under perturbation of a set of inputparameters. Specifically, we analyze the behavior of solutions on the centralpath with respect to changes on the right hand side of the...

In this paper we generalize the primal--dual cone affine scaling algorithm of Sturm and Zhang to semidefinite programming.We show in this paper that the underlying ideas of the cone affine scaling algorithm can be naturely applied to semidefiniteprogramming, resulting in a new algorithm....

We study disclosure of information about the multidimensional state of the world when uninformed receivers' actions affect the sender's utility. Given a disclosure rule, the receivers form an expectation about the state following each message. Under the assumption that the sender's expected...

In this paper, we develop various calculus rules for general smooth matrix-valued functions and for the class of matrix convex (or concave) functions first introduced by Loewner and Kraus in 1930s. Then we use these calculus rules and the matrix convex function -log X to study a new notion of...

Parameter uncertainty has been a recurrent subject treated in the financial literature. The normative portfolio selection approach considers two main kinds of decision rules: expected expected utility maximization and mean-variance criterion. Assuming that the mean-variance criterion is a good...

We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: [R.E....