An optimally fast objective-function-free minimization algorithm using random subspaces
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nonlinear optimization
Sequential Quadratic Optimization for Stochastic Optimization with Deterministic Nonlinear Inequality and Equality Constraints
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 tractable to evaluate constraint function and derivative values in each iteration, but it is intractable to evaluate the objective function or … Read more
On the paper “Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem”
In the paper [Torrealba, E.M.R. et al. Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem. EJOR, 299(1) 46–59, 2021] an augmented Lagrangian algorithm was proposed for resource allocation problems with the intriguing characteristic that instead of solving the box-constrained augmented Lagrangian subproblem, they propose projecting the solution of the unconstrained subproblem onto … Read more
Gas Transport Network Optimization: Mixed-Integer Nonlinear Models
Although modern societies strive towards energy systems that are entirely based on renewable energy carriers, natural gas is still one of the most important energy sources. This became even more obvious in Europe with Russia’s 2022 war against the Ukraine and the resulting stop of gas supplies from Russia. Besides that it is very important … Read more
Shape-Changing Trust-Region Methods Using Multipoint Symmetric Secant Matrices
In this work, we consider methods for large-scale and nonconvex unconstrained optimization. We propose a new trust-region method whose subproblem is defined using a so-called “shape-changing” norm together with densely-initialized multipoint symmetric secant (MSS) matrices to approximate the Hessian. Shape-changing norms and dense initializations have been successfully used in the context of traditional quasi Newton … Read more
A Quadratically Convergent Sequential Programming Method for Second-Order Cone Programs Capable of Warm Starts
We propose a new method for linear second-order cone programs. It is based on the sequential quadratic programming framework for nonlinear programming. In contrast to interior point methods, it can capitalize on the warm-start capabilities of active-set quadratic programming subproblem solvers and achieve a local quadratic rate of convergence. In order to overcome the non-differentiability … Read more
Convergence to a second-order critical point of composite nonsmooth problems by a trust region method
An algorithm for finding a first-order and second-order critical point of composite nonsmooth problems is proposed in this paper. For smooth problems, algorithms for searching such a point usually utilize the so called negative-curvature directions. In this paper, the method recently proposed for nonlinear semidefinite problems by the current author is extended for solving general … Read more
Worst-Case Complexity of TRACE with Inexact Subproblem Solutions for Nonconvex Smooth Optimization
An algorithm for solving nonconvex smooth optimization problems is proposed, analyzed, and tested. The algorithm is an extension of the Trust Region Algorithm with Contractions and Expansions (TRACE) [Math. Prog. 162(1):132, 2017]. In particular, the extension allows the algorithm to use inexact solutions of the arising subproblems, which is an important feature for solving large-scale … Read more
Advancements in the computation of enclosures for multi-objective optimization problems
A central goal for multi-objective optimization problems is to compute their nondominated sets. In most cases these sets consist of infinitely many points and it is not a practical approach to compute them exactly. One solution to overcome this problem is to compute an enclosure, a special kind of coverage, of the nondominated set. One … Read more
Improving the global convergence of Inexact Restoration methods for constrained optimization problems
Inexact restoration (IR) methods are an important family of numerical methods for solving constrained optimization problems with applications to electronic structures and bilevel programming among others areas. In these methods, the minimization is divided in two phases: decreasing infeasibility (feasibility phase) and improving optimality (optimality phase). The feasibility phase does not require the generated points … Read more