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A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
Model instability and poor prediction of long-term behavior are common problems when modeling dynamical systems using nonlinear "black-box" techniques. Direct optimization of the long-term predictions, often called simulation error…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
Parallel machine scheduling has been extensively studied in the past decades, with applications ranging from production planning to job processing in large computing clusters. In this work we study some of these fundamental optimization…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
A novel decomposition scheme to solve parametric non-convex programs as they arise in Nonlinear Model Predictive Control (NMPC) is presented. It consists of a fixed number of alternating proximal gradient steps and a dual update per time…
This paper provides necessary and sufficient optimality conditions for abstract constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geometrical properties of…
The reduction of constraints to obtain minimal representations of sets is a very common problem in many engineering applications. While well-established methodologies exist for the case of linear constraints, the problem of how to detect…
Control algorithms such as model predictive control (MPC) and state estimators rely on a number of different parameters. The performance of the closed loop usually depends on the correct setting of these parameters. Tuning is often done…
Adaptive cubic regularization methods have emerged as a credible alternative to linesearch and trust-region for smooth nonconvex optimization, with optimal complexity amongst second-order methods. Here we consider a general/new class of…
This paper presents a general convergence theory of penalty based numerical methods for elliptic constrained inequality problems, including variational inequalities, hemivariational inequalities, and variational-hemivariational…
Typically, the sequence of points generated by an optimization algorithm may have multiple limit points. Under convexity assumptions, however, (sub)gradient methods are known to generate a convergent sequence of points. In this paper, we…
We consider the nonconvex regularized method for low-rank matrix recovery. Under the assumption on the singular values of the parameter matrix, we provide the recovery bound for any stationary point of the nonconvex method by virtue of…
We propose a new disjunctive regularization for mathematical programs with complementarity constraints (MPCC). Its feasible set coincides with that of the Kanzow-Schwartz regularization. However, their functional descriptions differ…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
Polynomial optimization encompasses a broad class of problems in which both the objective function and constraints are polynomial functions of the decision variables. In recent years, a substantial body of research has focused on…
In this work we collect and compare to each other many different numerical methods for regularized regression problem and for the problem of projection on a hyperplane. Such problems arise, for example, as a subproblem of demand matrix…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
The conventional way of formulating inverse problems such as identification of a (possibly infinite dimensional) parameter, is via some forward operator, which is the concatenation of the observation operator with the parameter-to-state-map…
Reduction of combinatorial filters involves compressing state representations that robots use. Such optimization arises in automating the construction of minimalist robots. But exact combinatorial filter reduction is an NP-complete problem…