Related papers: A Partial Exact Penalty Function Approach for Cons…

This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…

The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…

In this paper, we study a variant of the quadratic penalty method for linearly constrained convex problems, which has already been widely used but actually lacks theoretical justification. Namely, the penalty parameter steadily increases…

Although well-established in general reinforcement learning (RL), value-based methods are rarely explored in constrained RL (CRL) for their incapability of finding policies that can randomize among multiple actions. To apply value-based…

Nonlinear power flow constraints render a variety of power system optimization problems computationally intractable. Emerging research shows, however, that the nonlinear AC power flow equations can be successfully modeled using Neural…

Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…

We present in this paper a novel approach for training deterministic auto-encoders. We show that by adding a well chosen penalty term to the classical reconstruction cost function, we can achieve results that equal or surpass those attained…

In this paper, we give an overview on optimality conditions and exact penalization for the mathematical program with switching constraints (MPSC). MPSC is a new class of optimization problems which has some important applications. It is…

The present paper contains some investigations about a uniform variant of the notion of metric hemiregularity, the latter being a less explored property obtained by weakening metric regularity. The introduction of such a quantitative…

This paper proposes an efficient adaptive variant of a quadratic penalty accelerated inexact proximal point (QP-AIPP) method proposed earlier by the authors. Both the QP-AIPP method and its variant solve linearly set constrained nonconvex…

Recently, deep unfolding methods that guide the design of deep neural networks (DNNs) through iterative algorithms have received increasing attention in the field of inverse problems. Unlike general end-to-end DNNs, unfolding methods have…

This paper focuses on a class of binary orthogonal optimization problems frequently arising in semantic hashing. Consider that this class of problems may have an empty feasible set, rendering them not well-defined. We introduce an…

In this work we present deep learning implementations of two popular theoretical constrained optimization algorithms in infinite dimensional Hilbert spaces, namely, the penalty and the augmented Lagrangian methods. We test these algorithms…

Linear Predictive Clustering (LPC) partitions samples based on shared linear relationships between feature and target variables, with numerous applications including marketing, medicine, and education. Greedy optimization methods, commonly…

This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…

This paper is concerned with optimal control problems for parabolic partial differential equations with pointwise in time switching constraints on the control. A standard approach to treat constraints in nonlinear optimization is…

We study settings where gradient penalties are used alongside risk minimization with the goal of obtaining predictors satisfying different notions of monotonicity. Specifically, we present two sets of contributions. In the first part of the…

This work studies the multi-task functional linear regression models where both the covariates and the unknown regression coefficients (called slope functions) are curves. For slope function estimation, we employ penalized splines to…

Two algorithms are proposed, analyzed, and tested for solving continuous optimization problems with nonlinear equality constraints. Each is an extension of a stochastic momentum-based method from the unconstrained setting to the setting of…

Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized…