Related papers: A survey of hidden convex optimization
In this note we aim at putting more emphasis on the fact that trying to solve non-convex optimization problems with coordinate-descent iterative linear matrix inequality algorithms leads to suboptimal solutions, and put forward other…
In this note, we focus on smooth nonconvex optimization problems that obey: (1) all local minimizers are also global; and (2) around any saddle point or local maximizer, the objective has a negative directional curvature. Concrete…
This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical…
The use of min-max optimization in adversarial training of deep neural network classifiers and training of generative adversarial networks has motivated the study of nonconvex-nonconcave optimization objectives, which frequently arise in…
In this work, we focus on separable convex optimization problems with linear and box constraints and compute the solution in closed-form as a function of some Lagrange multipliers that can be easily computed in a finite number of…
Convexification based on convex envelopes is ubiquitous in the non-linear optimization literature. Thanks to considerable efforts of the optimization community for decades, we are able to compute the convex envelopes of a considerable…
In this paper we first extend the diminishing stepsize method for nonconvex constrained problems presented in [4] to deal with equality constraints and a nonsmooth objective function of composite type. We then consider the particular case…
We present a nonlinear non-convex model predictive control approach to solving a real-world labyrinth game. We introduce adaptive nonlinear constraints, representing the non-convex obstacles within the labyrinth. Our method splits the…
Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic…
Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the…
In this paper, we propose an exact general algorithm for solving non-convex optimization problems, where the non-convexity arises due to the presence of an inverse S-shaped function. The proposed method involves iteratively approximating…
Problems related to projections on closed convex cones are frequently encountered in optimization theory and related fields. To study these problems, various unifying ideas have been introduced, including asymmetric vector-valued norms and…
Generalized polyhedral convex optimization problems in locally convex Hausdorff topological vector spaces are studied systematically in this paper. We establish solution existence theorems, necessary and sufficient optimality conditions,…
Motivated by modern regression applications, in this paper, we study the convexification of a class of convex optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work…
In the framework of shape constrained estimation, we review methods and works done in convex set estimation. These methods mostly build on stochastic and convex geometry, empirical process theory, functional analysis, linear programming,…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
We derive a closed-form expression for the projection onto a capped rotated second-order cone -- a convex set that arises in perspective relaxations of nonlinear programs with binary indicator variables. The closed-form solution involves…
We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a…