Related papers: Constrained local extrema without Lagrange multipl…
Constrained optimization offers a powerful framework to prescribe desired behaviors in neural network models. Typically, constrained problems are solved via their min-max Lagrangian formulations, which exhibit unstable oscillatory dynamics…
Systems subjected to holonomic constraints follow quite complicated dynamics that could not be described easily with Hamiltonian or Lagrangian dynamics. The influence of holonomic constraints in equations of motions is taken into account by…
A new Levenberg--Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM method have been proposed, their main differences being in the choice of a damping…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
In this paper, we propose a machine learning (ML) method to learn how to solve a generic constrained continuous optimization problem. To the best of our knowledge, the generic methods that learn to optimize, focus on unconstrained…
Variational problems under uniform quasiconvex constraints on the gradient are studied. In particular, existence of solutions to such problems is proved as well as existence of lagrange multipliers associated to the uniform constraint. They…
Cooperative geolocation has attracted significant research interests in recent years. A large number of localization algorithms rely on the availability of statistical knowledge of measurement errors, which is often difficult to obtain in…
This paper is devoted to the study of second order optimality conditions for strong local minimizers in the frameworks of unconstrained and constrained optimization problems in finite dimensions via subgradient graphical derivative. We…
In this paper, we propose an unconstrained framework for eigenvalue problems in both discrete and continuous settings. We begin our discussion to solve a generalized eigenvalue problem $A{\bf x} = \lambda B{\bf x}$ with two $N\times N$ real…
We provide a new proof of the linear convergence of the alternating direction method of multipliers (ADMM) when one of the objective terms is strongly convex. Our proof is based on a framework for analyzing optimization algorithms…
We consider the notions of (i) critical points, (ii) second-order points, (iii) local minima, and (iv) strict local minima for multivariate polynomials. For each type of point, and as a function of the degree of the polynomial, we study the…
An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy…
Functional constraints and bi-functional constraints are an important constraint class in Constraint Programming (CP) systems, in particular for Constraint Logic Programming (CLP) systems. CP systems with finite domain constraints usually…
Point source localisation is generally modelled as a Lasso-type problem on measures. However, optimisation methods in non-Hilbert spaces, such as the space of Radon measures, are much less developed than in Hilbert spaces. Most numerical…
Differential Dynamic Programming (DDP) has become a well established method for unconstrained trajectory optimization. Despite its several applications in robotics and controls however, a widely successful constrained version of the…
In this work, we focus on separable convex optimization problems with box constraints and a set of triangular linear constraints. The solution is given in closed-form as a function of some Lagrange multipliers that can be computed through…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
In this paper we present a finite element method for the direct transcription of constrained non-linear optimal control problems. We prove that our method converges of high order under mild assumptions. Our analysis uses a regularized…
The objective of this paper is to introduce and demonstrate a robust method for multi-constrained topology optimization. The method is derived by combining the topological sensitivity with the classic augmented Lagrangian formulation. The…
In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…