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We address the open problem of training hypernetworks for Controllable Pareto Front Learning (CPFL) under split feasibility conditions with rigorous theoretical guarantees. We reformulate the constrained Pareto problem as a Bi-Level…
Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach…
For solving constrained multicriteria problems, we introduce the multiobjective barrier method (MBM), which extends the scalar-valued internal penalty method. This multiobjective version of the classical method also requires a penalty…
Recent work has demonstrated that water supply pumps in the drinking water distribution network can be leveraged to provide flexibility to the power network, but existing approaches are computationally demanding and/or overly conservative.…
In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the iteratively reweighted alternating…
Consider a set of N agents seeking to solve distributively the minimization problem $\inf_{x} \sum_{n = 1}^N f_n(x)$ where the convex functions $f_n$ are local to the agents. The popular Alternating Direction Method of Multipliers has the…
We consider a method of pairwise variations for smooth optimization problems, which involve polyhedral constraints. It consists in making steps with respect to the difference of two selected extreme points of the feasible set together with…
We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss…
Several different ways exist for approaching hard optimization problems. Mathematical programming techniques, including (integer) linear programming-based methods and metaheuristic approaches, are two highly successful streams for…
Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization,…
In this paper, we present a new ensemble-based filter method by reconstructing the analysis step of the particle filter through a transport map, which directly transports prior particles to posterior particles. The transport map is…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
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…
Control synthesis under constraints is at the forefront of research on autonomous systems, in part due to its broad application from low-level control to high-level planning, where computing control inputs is typically cast as a constrained…
Saddle-point problems appear in various settings including machine learning, zero-sum stochastic games, and regression problems. We consider decomposable saddle-point problems and study an extension of the alternating direction method of…
We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework…
This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…
For multiparametric mixed-integer convex programming problems such as those encountered in hybrid model predictive control, we propose an algorithm for generating a feasible partition of a subset of the parameter space. The result is a…
For the efficient compensation of fiber nonlinearity, one of the guiding principles appears to be: fewer steps are better and more efficient. We challenge this assumption and show that carefully designed multi-step approaches can lead to…