Related papers: A Gap Penalty Reformulation for Mathematical Progr…
In this paper, we are concerned with stationarity conditions and qualification conditions for optimization problems with disjunctive constraints. This class covers, among others, optimization problems with complementarity, vanishing, or…
A class of exact penalty-type local search methods for optimal control problems with nonsmooth cost functional, nonsmooth (but continuous) dynamics, and nonsmooth state and control constraints is presented, in which the the penalty…
Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate…
This paper focuses on stochastic optimal control problems with constraints in law, which are rewritten as optimization (minimization) of probability measures problem on the canonical space. We introduce a penalized version of this type of…
In this paper we propose an Approximate Weak stationarity ($AW$-stationarity) concept designed to deal with {\em Mathematical Programs with Cardinality Constraints} (MPCaC), and we proved that it is a legitimate optimality condition…
This paper develops a method to obtain the optimal value for the regularization coefficient in a general mixed-integer problem (MIP). This approach eliminates the cross-validation performed in the existing penalty techniques to obtain a…
We propose new methods to speed up convergence of the Alternating Direction Method of Multipliers (ADMM), a common optimization tool in the context of large scale and distributed learning. The proposed method accelerates the speed of…
We consider minimization problems with structured objective function and smooth constraints, and present a flexible framework that combines the beneficial regularization effects of (exact) penalty and interior-point methods. In the fully…
This paper proposes a mechanism to produce equivalent Lipschitz surrogates for zero-norm and rank optimization problems by means of the global exact penalty for their equivalent mathematical programs with an equilibrium constraint (MPECs).…
Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal, then, is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
We consider the problem of minimizing a convex separable objective (as a separable sum of two proper closed convex functions $f$ and $g$) over a linear coupling constraint. We assume that $f$ can be decomposed as the sum of a smooth part…
In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction…
The symplectic eigenvalue problem for symmetric positive-definite (spd) matrices plays a crucial role in various scientific fields, including quantum mechanics and control theory. This paper introduces a trace-penalty minimization method,…
Solving linear programs by using entropic penalization has recently attracted new interest in the optimization community, since this strategy forms the basis for the fastest-known algorithms for the optimal transport problem, with many…
In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…
In this paper, we provide an elementary, geometric, and unified framework to analyze conic programs that we call the strict complementarity approach. This framework allows us to establish error bounds and quantify the sensitivity of the…
In recent years, bilevel approaches have become very popular to efficiently estimate high-dimensional hyperparameters of machine learning models. However, to date, binary parameters are handled by continuous relaxation and rounding…
The Model Predictive Control (MPC) scheme Funnel MPC enables output tracking of smooth reference signals with prescribed error bounds for nonlinear multi-input multi-output systems with stable internal dynamics. Earlier works achieved the…
We analyze the convergence of piecewise collocation methods for computing periodic solutions of general retarded functional differential equations under the abstract framework recently developed in [S. Maset, Numer. Math. (2016)…