Related papers: On implicit variables in optimization theory

In view of training increasingly complex learning architectures, we establish a nonsmooth implicit function theorem with an operational calculus. Our result applies to most practical problems (i.e., definable problems) provided that a…

We introduce a constructive method that provides the local solution of general implicit systems in arbitrary dimension via Hamiltonian type equations. A variant of this approach constructs parametrizations of the manifold, extending the…

High-performance dynamic language implementations make heavy use of speculative optimizations to achieve speeds close to statically compiled languages. These optimizations are typically performed by a just-in-time compiler that generates…

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…

A basic requirement for a mathematical model is often that its solution (output) shouldn't change much if the model's parameters (input) are perturbed. This is important because the exact values of parameters may not be known and one would…

Implicit computational complexity, which aims at characterizing complexity classes by machine-independent means, has traditionally been based, on the one hand, on programs and deductive formalisms for free algebras, and on the other hand on…

We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…

In optimization problems involving smooth functions and real and matrix variables, that contain matrix semidefiniteness constraints, consider the following change of variables: Replace the positive semidefinite matrix $X \in \mathbb{S}^d$,…

We consider a class of stochastic programs whose uncertain data has an exponential number of possible outcomes, where scenarios are affinely parametrized by the vertices of a tractable binary polytope. Under these conditions, we propose a…

The paper deals with the implicit programming approach to a class of Mathematical Programs with Equilibrium Constraints (MPECs) and bilevel programs in the case when the corresponding reduced problems are solved using a bundle method of…

Optimization problems with both control variables and environmental variables arise in many fields. This paper introduces a framework of personalized optimization to han- dle such problems. Unlike traditional robust optimization,…

With dramatic improvements in optimization software, the solution of large-scale problems that seemed intractable decades ago are now a routine task. This puts even more real-world applications into the reach of optimizers. At the same…

Usually, bilevel optimization problems need to be transformed into single-level ones in order to derive optimality conditions and solution algorithms. Among the available approaches, the replacement of the lower-level problem by means of…

Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…

Interatomic potentials are essential to go beyond ab initio size limitations, but simulation results depend sensitively on potential parameters. Forward propagation of parameter variation is key for uncertainty quantification, whilst…

We develop and analyze algorithms for instrumental variable regression by viewing the problem as a conditional stochastic optimization problem. In the context of least-squares instrumental variable regression, our algorithms neither require…

Multistage stochastic optimization problems are oftentimes formulated informally in a pathwise way. These are correct in a discrete setting and suitable when addressing computational challenges, for example. But the pathwise problem…

In this workshop, we present a compact but rigorous introduction to second-order optimality conditions for mathematical programs with equilibrium constraints (MPECs). We start from the classical nonlinear programming template, then explain…

In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…

Decision-theoretic planning with risk-sensitive planning objectives is important for building autonomous agents or decision-support systems for real-world applications. However, this line of research has been largely ignored in the…