In this paper, we consider a class of optimal control problems subject to equality terminal state constraints and continuous state and control inequality constraints. By using the control parametrization technique and a time scaling transformation, the constrained optimal control problem is approximated by a sequence of optimal parameter selection problems with equality terminal state constrain...

This short note considers and resolves the apparent contradiction between known worst-case complexity results for first and second-order methods for solving unconstrained smooth nonconvex optimization problems and a recent note by Jarre (2011) implying a very large lower bound on the number of iterations required to reach the solution’s neighbourhood for a specific problem with variable dimension.

This paper is concerned with the open problem whether BFGS method with inexact line search converges globally when applied to nonconvex unconstrained optimization problems. We propose a cautious BFGS update and prove that the method with either Wolfe-type or Armijo-type line search converges globally if the function to be minimized has Lipschitz continuous gradients.

As feature size is much smaller than the wavelength of illumination source of lithography equipments, resolution enhancement technology (RET) has been increasingly relied upon to minimize image distortions. In advanced process nodes, pixelated mask becomes essential for RET to achieve an acceptable resolution. In this paper, we investigate the problem of pixelated binary mask design in a partia...

The aim of angular super-resolution is to surpass the real-beam resolution. In this paper, a method for forward-looking scanning radar angular super-resolution imaging through a deconvolution method is proposed, which incorporates the prior information of the target’s scattering characteristics. We first mathematically formulate the angular super-resolution problem of forward-looking scanning r...

Initially, second-order necessary and sufficient optimality conditions in terms of Hadamard type derivatives for the unconstrained scalar optimization problem φ(x)→ min, x ∈ R, are given. These conditions work with arbitrary functions φ, but they show inconsistency with the classical derivatives. This is a base to pose the question, whether the formulated optimality conditions remain true when ...

Neural networks have been used prominently in several machine learning and statistics applications. In general, the underlying optimization of neural networks is non-convex which makes their performance analysis challenging. In this paper, we take a novel approach to this problem by asking whether one can constrain neural network weights to make its optimization landscape have good theoretical ...

Steepest descent preconditioning is considered for the recently proposed nonlinear generalized minimal residual (N-GMRES) optimization algorithm for unconstrained nonlinear optimization. Two steepest descent preconditioning variants are proposed. The first employs a line search, while the second employs a predefined small step. A simple global convergence proof is provided for the NGMRES optimi...

Generalized Nash equilibrium problems (GNEPs) allow, in contrast to standard Nash equilibrium problems, a dependence of the strategy space of one player from the decisions of the other players. In this paper, we consider jointly convex GNEPs which form an important subclass of the general GNEPs. Based on a regularized Nikaido-Isoda function, we present two (nonsmooth) reformulations of this cla...

An accelerated first-order method for solving SOS relaxations of unconstrained polynomial optimization problems Dimitris Bertsimas , Robert M. Freund & Xu Andy Sun To cite this article: Dimitris Bertsimas , Robert M. Freund & Xu Andy Sun (2013) An accelerated first-order method for solving SOS relaxations of unconstrained polynomial optimization problems, Optimization Methods and Software, 28:3...