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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...

Pareto efficiency for robust linear programs was introduced by Iancu and Trichakis in [Manage Sci 60(1):130–147, 9 ]. We generalize their approach and theoretical results to robust optimization problems in Euclidean spaces with affine uncertainty. Additionally, we demonstrate the value of this...

We introduce and study the class of semidefinite games, which generalizes bimatrix games and finite N -person games, by replacing the simplex of the mixed strategies for each player by a slice of the positive semidefinite cone in the space of real symmetric matrices. For semidefinite two-player...

We consider polynomial optimization problems pervaded by a sparsity pattern. It has been shown in [1, 2] that the optimal solution of a polynomial programming problem with structured sparsity can be computed by solving a series of semidefinite relaxations that possess the same kind of sparsity....

This paper proposes downside risk measure models in portfolio selection that captures uncertainties both in distribution and in parameters. The worst-case distribution with given information on the mean value and the covariance matrix is used, together with ellipsoidal and polytopic uncertainty...

In this paper, we propose a new deterministic global optimization method for solving nonlinear optimal control problems in which the constraint conditions of differential equations and the performance index are expressed as polynomials of the state and control functions. The nonlinear optimal...

The elegant theoretical results for strong duality and strict complementarity for linear programming, LP, lie behind the success of current algorithms. In addition, preprocessing is an essential step for efficiency in both simplex type and interior-point methods. However, the theory and...