Abstract Non-convex discrete-time optimal control problems in, e.g. , water or power systems, typically involve a large number of variables related through nonlinear equality constraints. The ideal goal is to find globally solution, and numerical experience indicates that algorithms aiming for Karush–Kuhn–Tucker points often solutions are indistinguishable from global optima. In our paper, we p...

We analyze two locational marginal pricing schemes in electricity markets derived from an economic dispatch (ED) problem with AC power flow equations that define a non-convex feasible set. The first among these prices, termed AC-LMPs, are Lagrange multipliers satisfy Karush-Kuhn-Tucker conditions for stationarity/local optimality of the ED problem. second, called SDP-LMPs, optimal dual semidefi...

The hybrid cellular automaton (HCA) algorithm was inspired by the structural adaptation of bones to their ever changing mechanical environment. This methodology has been shown to be an effective topology synthesis tool. In previous work, it has been observed that the convergence of the HCA methodology is affected by parameters of the algorithm. As a result, questions have been raised regarding ...

This paper proposes simple and computationally efficient forecasting algorithms for a KuhnTucker (KT) consumer demand model system called the Multiple Discrete-Continuous Extreme Value (MDCEV) model. The algorithms build on simple, yet insightful, analytical explorations with the Kuhn-Tucker conditions of optimality that shed new light on the properties of the model. Although developed for the ...

One important issue in the theory of Ordered Weighted Averaging (OWA) operators is the determination of the associated weights. One of the first approaches, suggested by O’Hagan, determines a special class of OWA operators having maximal entropy of the OWA weights for a given level of orness; algorithmically it is based on the solution of a constrained optimization problem. Another consideratio...

Computation of general stateand/or control-constrained Optimal Control Problems (OCPs) is difficult for various constraints, especially the intractable path constraint. For such problems, the theoretical convergence of numerical algorithms is usually not guaranteed, and the right solution may not be successfully obtained. With the recently proposed Variation Evolving Method (VEM), the evolution...

2-band paraunitary FIR lter banks can be used to generate a multiresolution analysis with compactly supported orthonormal (ON) wavelets. The lter design problem is formulated and solved (a) as a constrained L1 optimization problem and (b) as a constrained L2 optimization problem which allows arbitrary compromises between an L2 and an L1 approach with both of them as special cases. Additional at...

We consider optimality systems of Karush-Kuhn-Tucker (KKT) type, which arise, for example, as primal-dual conditions characterizing solutions of optimization problems or variational inequalities. In particular, we discuss error bounds and Newton-type methods for such systems. An exhaustive comparison of various regularity conditions which arise in this context is given. We obtain a new error bo...

This note presents a new approach to deriving stability conditions for continuous-time linear systems interconnected with a saturation. The method presented here can be extended to handle a deadzone, or in general, nonlinearities in the form of piecewise linear functions. By representing the saturation as a constrained optimization problem, the necessary (Kuhn–Tucker) conditions for optimality ...

The abuse of market power is a potentially serious problem for market designers. Few if any indices exist to measure the potential for market power in real-time. In references [1-2] an expression for a dispatch-to-price sensitivity matrix, M, was derived. The expression requires information about network topology and parameters as well as the rules used to operate the market. While computing th...