We discuss minimization of a smooth function to which is added a separable regularization function that induces structure in the solution. A block-coordinate relaxation approach with proximal linearized subproblems yields convergence to critical points, while identification of the optimal manifold (under a nondegeneracy condition) allows acceleration techniques to be applied on a reduced space. The … Read more
An artificial neural network (ANN) is a computational model – implemented as a computer program – that is aimed at emulating the key features and operations of biological neural networks. ANNs are extensively used to model unknown or unspecified functional relationships between the input and output of a “black box” system. In order to apply … Read more
In this paper we present a generic algorithmic framework, namely, the accelerated stochastic approximation (AC-SA) algorithm, for solving strongly convex stochastic composite optimization (SCO) problems. While the classical stochastic approximation (SA) algorithms are asymptotically optimal for solving differentiable and strongly convex problems, the AC-SA algorithm, when employed with proper stepsize policies, can achieve optimal or … Read more
A Euclidean distance matrix is one in which the $(i,j)$ entry specifies the squared distance between particle $i$ and particle $j$. Given a partially-specified symmetric matrix $A$ with zero diagonal, the Euclidean distance matrix completion problem (EDMCP) is to determine the unspecified entries to make $A$ a Euclidean distance matrix. We survey three different approaches … Read more
We present a new algorithm for nonnegative least-squares (NNLS). Our algorithm extends the unconstrained quadratic optimization algorithm of Barzilai and Borwein (BB) (J. Barzilai and J. M. Borwein; Two-Point Step Size Gradient Methods. IMA J. Numerical Analysis; 1988.) to handle nonnegativity constraints. Our extension diff ers in several basic aspects from other constrained BB variants. The … Read more
We consider robust output feedback control of time-varying, linear discrete-time systems operating over a finite horizon. For such systems, we consider the problem of designing robust causal controllers that minimize the expected value of a convex quadratic cost function, subject to mixed linear state and input constraints. Determination of an optimal control policy for such … Read more
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