We present a numerical method for solving tracking-type optimal control problems subject to scalar nonlinear hyperbolic balance laws in one and two space dimensions. Our approach is based on the formal optimality system and requires numerical solutions of the hyperbolic balance law forward in...

<Para ID="Par1">Sequential quadratic programming (SQP) methods are known to be efficient for solving a series of related nonlinear optimization problems because of desirable hot and warm start properties—a solution for one problem is a good estimate of the solution of the next. However, standard SQP solvers...</para>

<Para ID="Par1">Recent years have seen growing interest in coherent risk measures, especially in Conditional Value-at-Risk (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mathrm {CVaR}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="normal">CVaR</mi> </math> </EquationSource> </InlineEquation>). Since <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\mathrm {CVaR}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="normal">CVaR</mi> </math> </EquationSource> </InlineEquation> is a convex function, it is suitable as an objective for optimization problems when we desire to minimize risk. In the...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></para>

The paper proposes a primal-dual algorithm for solving an equality constrained minimization problem. The algorithm is a Newton-like method applied to a sequence of perturbed optimality systems that follow naturally from the quadratic penalty approach. This work is first motivated by the fact...

We propose a new gradient method for quadratic programming, named SDC, which alternates some steepest descent (SD) iterates with some gradient iterates that use a constant steplength computed through the Yuan formula. The SDC method exploits the asymptotic spectral behaviour of the Yuan...

In this paper, we propose a robust sequential quadratic programming (SQP) method for nonlinear programming without using any explicit penalty function and filter. The method embeds the modified QP subproblem proposed by Burke and Han (Math Program 43:277–303, <CitationRef CitationID="CR9">1989</CitationRef>) for the search direction,...</citationref>

We consider a regularized least squares problem, with regularization by structured sparsity-inducing norms, which extend the usual ℓ <Subscript>1</Subscript> and the group lasso penalty, by allowing the subsets to overlap. Such regularizations lead to nonsmooth problems that are difficult to optimize, and we propose...</subscript>

The linear spline regression problem is to determine a piecewise linear function for estimating a set of given points while minimizing a given measure of misfit or error. This is a classical problem in computational statistics and operations research; dynamic programming was proposed as a...

A minimum effort optimal control problem for the undamped wave equation is considered which involves L <Superscript>∞</Superscript>-control costs. Since the problem is non-differentiable a regularized problem is introduced. Uniqueness of the solution of the regularized problem is proven and the convergence of the...</superscript>

We consider a two-stage defender-attacker game that takes place on a network, in which the attacker seeks to take control over (or “influence”) as many nodes as possible. The defender acts first in this game by protecting a subset of nodes that cannot be influenced by the attacker. With full...