Related papers: Successive Convexification with Feasibility Guaran…
This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…
We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…
This work considers the decentralized successive convex approximation (SCA) method for minimizing stochastic non-convex objectives subject to convex constraints, along with possibly non-smooth convex regularizers. Although SCA has been…
In the article we present a general theory of augmented Lagrangian functions for cone constrained optimization problems that allows one to study almost all known augmented Lagrangians for cone constrained programs within a unified…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
We consider stochastic optimization problems with non-convex functional constraints, such as those arising in trajectory generation, sparse approximation, and robust classification. To this end, we put forth a recursive momentum-based…
Dual decomposition is a powerful technique for deriving decomposition schemes for convex optimization problems with separable structure. Although the Augmented Lagrangian is computationally more stable than the ordinary Lagrangian, the…
First-order methods (FOMs) have been widely used for solving large-scale problems. A majority of existing works focus on problems without constraint or with simple constraints. Several recent works have studied FOMs for problems with…
We introduce a framework for designing primal methods under the decentralized optimization setting where local functions are smooth and strongly convex. Our approach consists of approximately solving a sequence of sub-problems induced by…
In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full…
Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…
A novel augmented Lagrangian method for solving non-convex programs with nonlinear cost and constraint couplings in a distributed framework is presented. The proposed decomposition algorithm is made of two layers: The outer level is a…
The auxiliary problem principle of augmented Lagrangian (APP-AL), proposed by Cohen and Zhu (1984), aims to find the solution of a constrained optimization problem through a sequence of auxiliary problems involving augmented Lagrangian. The…
This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…
Motion planning for manipulators under task space constraints is difficult as it constrains the joint configurations to always lie on an implicitly defined manifold. It is possible to view task constrained motion planning as an optimization…
This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with…
Clustering may be the most fundamental problem in unsupervised learning which is still active in machine learning research because its importance in many applications. Popular methods like K-means, may suffer from instability as they are…
We introduce a verification framework to exactly verify the worst-case performance of sequential convex programming (SCP) algorithms for parametric non-convex optimization. The verification problem is formulated as an optimization problem…
In this paper, we propose an algorithm for optimal generation of nonholonomic paths for planning parking maneuvers with a kinematic car model. We demonstrate the use of Successive Convexification algorithms (SCvx), which guarantee path…
In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of…