Related papers: Lossless convexification of non-convex optimal con…
We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set…
Economic dispatch problem for a networked power system has been considered. The objective is to minimize the total generation cost while meeting the overall supply-demand balance and generation capacity. In particular, a more practical…
This paper first proposes an N-block PCPM algorithm to solve N-block convex optimization problems with both linear and nonlinear constraints, with global convergence established. A linear convergence rate under the strong second-order…
This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The…
The min-max optimization problem, also known as the saddle point problem, is a classical optimization problem which is also studied in the context of zero-sum games. Given a class of objective functions, the goal is to find a value for the…
In the area of sparse recovery, numerous researches hint that non-convex penalties might induce better sparsity than convex ones, but up until now those corresponding non-convex algorithms lack convergence guarantees from the initial…
We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially…
In this paper, we introduce a class of nonsmooth nonconvex least square optimization problem using convex analysis tools and we propose to use the iterative minimization-majorization (MM) algorithm on a convex set with initializer away from…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…
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…
Computing optimal, collision-free trajectories for high-dimensional systems is a challenging problem. Sampling-based planners struggle with the dimensionality, whereas trajectory optimizers may get stuck in local minima due to inherent…
The pooling problem has applications, e.g., in petrochemical refining, water networks, and supply chains and is widely studied in global optimization. To date, it has largely been treated deterministically, neglecting the influence of…
We introduce a convex optimization modeling framework that transforms a convex optimization problem expressed in a form natural and convenient for the user into an equivalent cone program in a way that preserves fast linear transforms in…
We consider a non-convex constrained Lagrangian formulation of a fundamental bi-criteria optimization problem for variable selection in statistical learning; the two criteria are a smooth (possibly) nonconvex loss function, measuring the…
We investigate the effectiveness of convex relaxation and nonconvex optimization in solving bilinear systems of equations under two different designs (i.e.$~$a sort of random Fourier design and Gaussian design). Despite the wide…
We propose an exact polynomial algorithm for a resource allocation problem with convex costs and constraints on partial sums of resource consumptions, in the presence of either continuous or integer variables. No assumption of strict…
Optimal control of switched systems is challenging due to the discrete nature of the switching control input. The embedding-based approach addresses this challenge by solving a corresponding relaxed optimal control problem with only…
This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices $\text{SO}(n)$. Such problems are nonconvex due to the constraint $X \in \text{SO}(n)$. Nonetheless, we show…
Solving optimal control problems (OCPs) of autonomous agents operating under spatial and temporal constraints fast and accurately is essential in applications ranging from eco-driving of autonomous vehicles to quadrotor navigation. However,…