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Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic,…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Common computational problems, such as parameter estimation in dynamic models and PDE constrained optimization, require data fitting over a set of auxiliary parameters subject to physical constraints over an underlying state. Naive…
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…
For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…
In this paper we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints, are locally smooth. For solving this problem, we propose a…
This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…
We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range…
We investigate non-convex optimization problems in $BV(\Omega)$ with two-sided pointwise inequality constraints. We propose a regularization and penalization method to numerically solve the problem. Under certain conditions, weak limit…
We construct an efficient numerical scheme for solving obstacle problems in divergence form. The numerical method is based on a reformulation of the obstacle in terms of an L1-like penalty on the variational problem. The reformulation is an…
In this work, the joint use of a mixed penalty-interior point method and direct search is proposed, to address {nonlinear} constrained derivative-free optimization problems. A merit function is considered, wherein the set of nonlinear…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
Learning-based control methods for industrial processes leverage the repetitive nature of the underlying process to learn optimal inputs for the system. While many works focus on linear systems, real-world problems involve nonlinear…
A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…
Optimization problems emerging in most of the real-world applications are dynamic, where either the objective function or the constraints change continuously over time. This paper proposes projected primal-dual dynamical system approaches…
This paper offers a unified perspective on different approaches to the solution of optimal control problems through the lens of constrained sequential quadratic programming. In particular, it allows us to find the relationships between…
Quadratic Unconstrained Binary Optimization models are useful for solving a diverse range of optimization problems. Constraints can be added by incorporating quadratic penalty terms into the objective, often with the introduction of slack…
A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is…