Related papers: Optimality Conditions for Cardinality-Constrained …
Many discrete optimization problems are amenable to constrained shortest-path reformulations in an extended network space, a technique that has been key in convexification, bound strengthening, and search. In this paper, we propose a…
Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices and the KKT conditions. It was shown in Burer(2009) that mixed-binary quadratic programs…
Portfolio optimization involves selecting asset weights to minimize a risk-reward objective, such as the portfolio variance in the classical minimum-variance framework. Sparse portfolio selection extends this by imposing a cardinality…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…
We consider a special class of nonconvex semidefinite programming problems and show that every point satisfying the Karush--Kuhn--Tucker (KKT) conditions is globally optimal despite nonconvexity. This property is related to pseudoconvex…
We propose a random coordinate descent algorithm for optimizing a non-convex objective function subject to one linear constraint and simple bounds on the variables. Although it is common use to update only two random coordinates…
We consider a smooth pessimistic bilevel optimization problem, where the lower-level problem is convex and satisfies the Slater constraint qualification. These assumptions ensure that the Karush-Kuhn-Tucker (KKT) reformulation of our…
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…
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 consider optimization problems in which the goal is find a $k$-dimensional subspace of $\mathbb{R}^n$, $k<<n$, which minimizes a convex and smooth loss. Such problems generalize the fundamental task of principal component analysis (PCA)…
The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely…
A memory-efficient framework is described for the cardinality-constrained structured data-fitting problem. Dual-based atom-identification rules are proposed that reveal the structure of the optimal primal solution from near-optimal dual…
In this paper, we consider a chance-constrained formulation of the optimal power flow problem to handle uncertainties resulting from renewable generation and load variability. We propose a tuning method that iterates between solving an…
When the lower-level optimal solution set-valued mapping of a bilevel optimization problem is not single-valued, we are faced with an ill-posed problem, which gives rise to the optimistic and pessimistic bilevel optimization problems, as…
One key challenge for solving a general stochastic optimization problem with expectations in the objective and constraint functions using ordinary stochastic iterative methods lies in the infeasibility issue caused by the randomness over…
We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of…
We characterize approximate global optimal solutions (${\varepsilon}$-optima) to reverse optimization problems, namely, problems whose non-convex constraint is of the form $h(x) \geq 0$. This issue has not been addressed previously in the…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
Minimax optimization problems are an important class of optimization problems arising from both modern machine learning and from traditional research areas. We focus on the stability of constrained minimax optimization problems based on the…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…