This paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main focus is the so-called (full and partial) second-order subdifferentials of extended-real-valued functions, which are dual-type constructions generated by coderivatives of first-order...

We investigate nonlinear pre-equalization techniques for the downlink of multiuser systems from a transmitter equipped with multiple antennas to noncooperative single antenna mobile receivers. Besides linear Multiuser Transmission (MUT), known as Transmit Zero Forcing or Transmit Wiener Filters, recently nonlinear Minimum Bit Error Rate (BER) MUT was proposed. The latter computes the transmit s...

We introduce a method for constrained nonlinear programming, that is widely used in mechanical engineering and that is known under the name SCP for sequential convex programming. The algorithm consists of solving a sequence of convex and separable subproblems, where an augmented Lagrangian merit function is used for guaranteeing convergence. Originally, SCP methods were developed in structural ...

In this paper we analyze the application of Newton's method to the solution of systems of nonlinear equations arising from equivalent forms of the rst{order Karush{Kuhn{Tucker necessary conditions for constrained optimization. The analysis is carried out by using an abstract model for the original system of nonlinear equations and for an equivalent form of this system obtained by a reformulatio...

In this paper we consider the problem of analyzing the stability of a discrete time nonlinear system in quasi-LPV form under an optimization based controller subject to constraints. We show that by representing the control law, which is computed on-line as the solution to a constrained optimization problem, by the Kuhn-Tucker conditions, stability questions can be reformulated as implications. ...

iii 1 Background and Significance 1 2 Preliminary Studies 3 2.1 PDE Time Integrators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 PDE Nonlinear Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 PDE-constrained Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Linear Solvers . . . ...

In this study, a flexible optimization approach is introduced to design an optimal biocompatible solvent for an extractive fermentation process with cell-recycling. The optimal process/solvent design problem is formulated as a mixed-integer nonlinear programming model in which performance requirements of the compounds are reflected in the objectives and the constraints. A flexible or fuzzy opti...

A novel segmentation algorithm has been developed utilizing an absolutevalue smoothness penalty instead of the more common quadratic regularizer. This functional imposes a piece-wise constant constraint on the segmented data. Since the minimized energy is guaranteed to be convex, there are no problems with local minima and no complex continuation methods are necessary to find the unique global ...

In a recent paper (Cartis Gould and Toint, Math. Prog. A 144(1-2) 93–106, 2014), the evaluation complexity of an algorithm to find an approximate first-order critical point for the general smooth constrained optimization problem was examined. Unfortunately, the proof of Lemma 3.5 in that paper uses a result from an earlier paper in an incorrect way, and indeed the result of the lemma is false. ...