We propose a fast population game dynamics, motivated by the analogy with infection and immunization processes within a population of “players,” for finding dominant sets, a powerful graph-theoretical notion of a cluster. Each step of the proposed dynamics is shown to have a linear time/space complexity and we show that, under the assumption of symmetric … Read more
In this paper we propose randomized first-order algorithms for solving bilinear saddle points problems. Our developments are motivated by the need for sublinear time algorithms to solve large-scale parametric bilinear saddle point problems where cheap online assessment of solution quality is crucial. We present the theoretical efficiency estimates of our algorithms and discuss a number … Read more
We propose a new look at the problem of truss topology optimization with integer or binary variables. We show that the problem can be equivalently formulated as an integer \emph{linear} semidefinite optimization problem. This makes its numerical solution much easier, compared to existing approaches. We demonstrate that one can use an off-the-shelf solver with default … Read more
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little demand on computer resources. For other problems, such as finding that point in the intersection at which the … Read more
We present new insights into how to achieve higher frequencies in large-scale nonlinear predictive control using truncated-like schemes. The basic idea is that, instead of solving the full nonlinear programming (NLP) problem at each sampling time, we solve a single, truncated quadratic programming (QP) problem. We present conditions guaranteeing stability of the approximation error derived … Read more
Inferences need to be drawn in biological systems using experimental multivariate data. The number of samples collected in many such experiments is small, and the data is noisy. We present and study the performance of a robust optimization (RO) model for such situations. We adapt this model to generate a minimum and a maximum estimation … Read more
The matrix completion problem is to recover a low-rank matrix from a subset of its entries. The main solution strategy for this problem has been based on nuclear-norm minimization which requires computing singular value decompositions — a task that is increasingly costly as matrix sizes and ranks increase. To improve the capacity of solving large-scale … Read more
In this paper we generalize to an arbitrary order, under minimal hypotheses, some sufficient conditions for Lipschitz continuity of the solution of a state constrained optimal control problems. The proof combines the approach by Hager in 1979 for dealing with first-order state constraints, and the high-order alternative formulation of the optimality conditions. Citation Published as … Read more
We develop and investigate two preconditioners for a basic linear iterative splitting method for the numerical solution of linear-quadratic optimization problems with time-periodic parabolic PDE constraints. The resulting real-valued linear system to be solved is symmetric indefinite. We propose all-at-once symmetric indefinite preconditioners based on a Newton–Picard approach which divides the variable space into slow … Read more
Traditional two-stage stochastic programming is risk-neutral; that is, it considers the expectation as the preference criterion while comparing the random variables (e.g., total cost) to identify the best decisions. However, in the presence of variability risk measures should be incorporated into decision making problems in order to model its effects. In this study, we consider … Read more