Related papers: Subdifferentials and penalty approximations of the…

This paper identifies necessary and sufficient conditions for the exactness of penalty functions in optimization problems whose constraint sets are not necessarily bounded. The case where the data of problems is locally Lipschitz,…

Penalized methods are applied to quasi likelihood analysis for stochastic differential equation models. In this paper, we treat the quasi likelihood function and the associated statistical random field for which a polynomial type large…

We consider an optimization problem with strongly convex objective and linear inequalities constraints. To be able to deal with a large number of constraints we provide a penalty reformulation of the problem. As penalty functions we use a…

The paper concerns optimization problems with general equality and inequality constraints and with constraints expressed by a convex set. In order to solve these problems, the general constraints are treated by an exact penalty functions…

In this two-part study we develop a general approach to the design and analysis of exact penalty functions for various optimal control problems, including problems with terminal and state constraints, problems involving differential…

We consider a system of semi-linear partial differential equations with measurable coefficients and a nonlinear Neumann boundary condition. We then construct a sequence of penalized partial differential equations which converges to a…

Feasibility pumps are highly effective primal heuristics for mixed-integer linear and nonlinear optimization. However, despite their success in practice there are only few works considering their theoretical properties. We show that…

In this paper, we develop a self-adaptive ADMM that updates the penalty parameter adaptively. When one part of the objective function is strongly convex i.e., the problem is semi-strongly convex, our algorithm can update the penalty…

A burgeoning line of research leverages deep neural networks to approximate the solutions to high dimensional PDEs, opening lines of theoretical inquiry focused on explaining how it is that these models appear to evade the curse of…

Recent efforts to develop trustworthy AI systems have increased interest in learning problems with explicit requirements, or constraints. In deep learning, however, such problems are often handled through fixed weighted-sum penalization:…

It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem…

We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…

Spline basis exploration via Bayesian model selection is a widely employed strategy for determining the optimal set of basis terms in nonparametric regression. However, despite its widespread use, this approach often encounters performance…

Submodular maximization generalizes many fundamental problems in discrete optimization, including Max-Cut in directed/undirected graphs, maximum coverage, maximum facility location and marketing over social networks. In this paper we…

We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…

In this paper we first study the penalization approximation of stochastic differential equations reflected in a domain which satisfies conditions (A) and (B) and prove that the sequence of solutions of the penalizing equations converges in…

We propose a class of numerical schemes for nonlocal HJB variational inequalities (HJBVIs) with monotone drivers. The solution and free boundary of the HJBVI are constructed from a sequence of penalized equations, for which a continuous…

We build upon Estrin et al. (2019) to develop a general constrained nonlinear optimization algorithm based on a smooth penalty function proposed by Fletcher (1970, 1973b). Although Fletcher's approach has historically been considered…

People tend to behave inconsistently over time due to an inherent present bias. As this may impair performance, social and economic settings need to be adapted accordingly. Common tools to reduce the impact of time-inconsistent behavior are…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…