A viscous discrete adjoint approach to automatic aerodynamic shape optimization is developed, and the merits of the viscous discrete and continuous adjoint approaches are discussed. The viscous discrete and continuous adjoint gradients for inverse design and drag minimization cost functions are compared with finite-difference and complex-step gradients. The optimization of airfoils in two-dimen...

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimiz...

OF THE DISSERTATION Distributed Optimization in Multi-Agent Systems: Game Theory Based Sensor Coverage and continuous-time Convex Optimization by Salar Rahili Doctor of Philosophy, Graduate Program in Electrical Engineering University of California, Riverside, December 2016 Dr. Wei Ren, Chairperson A multi-agent system is defined as a collection of autonomous agents which are able to interact w...

The minimum sum-of-squared error clustering problem is shown to be a concave continuous optimization problem whose every local minimum solution must be integer. We characterize its local minima. A procedure of moving from a fractional solution to a better integer solution is given. Then we adapt Tuy’s convexity cut method to find a global optimum of the minimum sum-of-squared error clustering p...

An important form of prior information in clustering comes in form of cannot-link and must-link constraints. We present a generalization of the popular spectral clustering technique which integrates such constraints. Motivated by the recently proposed 1-spectral clustering for the unconstrained problem, our method is based on a tight relaxation of the constrained normalized cut into a continuou...

While multi-agent systems have been successfully applied to combinatorial optimization, very few works concern their applicability to continuous optimization problems. In this article we propose a framework for modeling a continuous optimization problems as multi-agent system, which we call NDMO, by representing the problem as an agent graph, and complemented with optimization solving behaviors...

In this paper, a new scheduling approach is proposed that considers the effect of modeling uncertainty for multiple continuous time receding horizon control (RHC) systems. This is accomplished by combining a scheduling approach with results from the continuous time nonlinear systems theory. It is shown that using a rate monotonic priority assignment method combined with analytical bounds on the...

The calculation of compatibility measures is an important technique employed in group decision-making with interval multiplicative preference relations. In this paper, a new compatibility measure called the continuous logarithm compatibility, which considers risk attitudes in decision-making based on the continuous ordered weighted geometric averaging (COWGA) operator, is introduced. We also de...

Motivated by a problem in music theory of measuring the distance between chords and scales we consider algorithms for obtaining a minimum-weight many-to-many matching between two sets of points on the real line. Given sets A and B, we want to find the best rigid translation of B and a many-to-many matching that minimizes the sum of the squares of the distances between matched points. We provide...