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A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…

Model predictive control (MPC) is a powerful framework for optimal control of dynamical systems. However, MPC solvers suffer from a high computational burden that restricts their application to systems with low sampling frequency. This…

Convex variational problems arise in many fields ranging from image processing to fluid and solid mechanics communities. Interesting applications usually involve non-smooth terms which require well-designed optimization algorithms for their…

This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…

This paper considers mathematical programs, whose constraints are expressed by a parameterized vector equilibrium problem. The latter is a well recognized framework, which is able to cover multicriteria optimization, vector variational…

Microfluidic devices manufactured from soft polymeric materials have emerged as a paradigm for cheap, disposable and easy-to-prototype fluidic platforms for integrating chemical and biological assays and analyses. The interplay between the…

Nonlinear convex problems arise in various areas of applied mathematics and engineering. Classical techniques such as the relaxed proximal point algorithm (PPA) and the prediction correction (PC) method were proposed for linearly…

In this paper, we consider a monolithic approach to handle coupled fluid-structure interaction problems with different hyperelastic models in an all-at-once manner. We apply Newton's method in the outer iteration dealing with nonlinearities…

Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…

In this paper, we propose new proximal Newton-type methods for convex optimization problems in composite form. The applications include model predictive control (MPC) and embedded MPC. Our new methods are computationally attractive since…

We describe and analyze an interior-point method to decide feasibility problems of second-order conic systems. A main feature of our algorithm is that arithmetic operations are performed with finite precision. Bounds for both the number of…

This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The…

We present a short step interior point method for solving a class of nonlinear programming problems with quadratic objective function. Convex quadratic programming problems can be reformulated as problems in this class. The method is shown…

We leverage path differentiability and a recent result on nonsmooth implicit differentiation calculus to give sufficient conditions ensuring that the solution to a monotone inclusion problem will be path differentiable, with formulas for…

This paper addresses the study of a new class of nonsmooth optimization problems, where the objective is represented as a difference of two generally nonconvex functions. We propose and develop a novel Newton-type algorithm to solving such…

Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond optimization to systems involving partly smooth operators, and in particular to…

We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…

We present a framework for the simulation of rigid and deformable bodies in the presence of contact and friction. Our method is based on a non-smooth Newton iteration that solves the underlying nonlinear complementarity problems (NCPs)…

This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a…

We consider adaptive control problem in presence of nonlinear parametrization of uncertainties in the model. It is shown that despite traditional approaches require for domination in the control loop during adaptation, it is not often…