SIAM Journal on Optimization

We consider a class of nonsmooth optimization problems over the Stiefel manifold, in which the objective function is weakly convex in the ambient Euclidean space. Such problems are ubiquitous in engineering applications but still largely unexplored. We ...

In this paper, we investigate the Moreau envelope of the supremum of a family of convex, proper, and lower semicontinuous functions. Under mild assumptions, we prove that the Moreau envelope of a supremum is the supremum of Moreau envelopes, which allows ...

Shape optimization based on shape calculus has received a lot of attention in recent years, particularly regarding the development, analysis, and modification of efficient optimization algorithms. In this paper we propose and investigate nonlinear ...

Recently, there has been a growing interest in distributionally robust optimization (DRO) as a principled approach to data-driven decision making. In this paper, we consider a distributionally robust two-stage stochastic optimization problem with discrete ...

Fundamental in matrix algebra and its applications, a generalized inverse of a real matrix $A$ is a matrix $H$ that satisfies the Moore--Penrose (M--P) property $AHA=A$. If $H$ also satisfies the additional useful M--P property, $HAH=H$, it is called a ...

In this paper, we adopt the augmented Lagrangian method (ALM) to solve convex quadratic second-order cone programming problems (SOCPs). Fruitful results on the efficiency of the ALM have been established in the literature. Recently, it has been shown in [...

Various characterizations of convexity for images of a vector mapping where some of its components are quadratic and the remaining ones are linear are established. In a certain sense, one might conclude that convexity of the full image is reduced to the ...

In this paper, through an intuitive vanilla proximal method perspective, we derive a concise unified acceleration framework (UAF) for minimizing a convex function that has Hölder continuous derivatives with respect to general (non-Euclidean) norms. The ...

Symmetries of a set are linear transformations that map the set to itself. A fundamental domain of a symmetric set is a subset that contains at least one representative from each of the symmetric equivalence classes (orbits) in the set. This paper ...

An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels in the MG/OPT hierarchy correspond to discretization levels of the PDE, ...

We consider a nonconvex optimization problem consisting of maximizing the difference of two convex functions. We present a randomized method that requires low computational effort at each iteration. The described method is a randomized coordinate descent ...

We consider the problem of estimating the true values of a Wiener process given noisy observations corrupted by outliers. In this paper we show how to improve existing mixed-integer quadratic optimization formulations for this problem. Specifically, we ...

Using the Attouch--Théra duality, we study the cycles, gap vectors, and fixed point sets of compositions of proximal mappings. Sufficient conditions are given for the existence of cycles and gap vectors. A primal-dual framework provides an exact ...

This article proposes an algorithm for convex programming which can be viewed as a further development of the method of alternating projections. Some combinatorial problems like the maximum matchings and the maximum simple $b$-matchings can be solved in ...

The adaptive Douglas--Rachford splitting algorithm iteratively applies the operator $T=\kappa_{n}Q_{A}Q_{B}+(1-\kappa_{n}){Id}$ to solve the inclusion problem $\text{zer}(A+B)$. By taking a Yosida approximation standpoint, we express in canonical form $Q_{A}...

We present a first-order quadratic cone programming algorithm that can scale to very large problem sizes and produce modest accuracy solutions quickly. Our algorithm returns primal-dual optimal solutions when available or certificates of infeasibility ...

In this paper, we study the sequential convex programming method with monotone line search (SCP$_{ls}$) in [Z. Lu, Sequential Convex Programming Methods for a Class of Structured Nonlinear Programming, ŭlhttps://arxiv.org/abs/1210.3039, 2012] for a class ...

Multi-leader-follower games are models which combine bilevel programming with generalized Nash games. Due to their many applications, they have attracted more and more attention in the last few years. We introduce here a particular case of the so-called ...

The classical Clarke subdifferential alone is inadequate for understanding automatic differentiation in nonsmooth contexts. Instead, we can sometimes rely on enlarged generalized gradients called “conservative fields,” defined through the natural ...

In [V. Guigues, SIAM J. Optim., 30 (2020), pp. 407--438], an inexact variant of stochastic dual dynamic programming (SDDP) called ISDDP was introduced which uses approximate (instead of exact with SDDP) primal dual solutions of the problems solved in the ...

Multistage stochastic programming deals with operational and planning problems that involve a sequence of decisions over time while responding to an uncertain future. Algorithms designed to address multistage stochastic linear programming (MSLP) problems ...

In this work, we consider a constrained convex problem with linear inequalities and provide an inexact penalty reformulation of the problem. The novelty is in the choice of the penalty functions, which are smooth and can induce a nonzero penalty over some ...

We consider a class of optimization problems with Cartesian variational inequality (CVI) constraints, where the objective function is convex and the CVI is associated with a monotone mapping and a convex Cartesian product set. This mathematical ...

We propose and analyze a versatile and general algorithm called nonlinear forward-backward splitting (NOFOB). The algorithm consists of two steps; first an evaluation of a nonlinear forward-backward map followed by a relaxed projection onto the separating ...

We investigate two classes of multivariate polynomials with variables indexed by the edges of a uniform hypergraph and coefficients depending on certain patterns of unions of edges. These polynomials arise naturally to model job-occupancy in some ...

We extend a sequential quadratic programming method for equality constrained optimization to the setting of Hilbert manifolds. The use of retractions and linearizing maps allows us to pull back the functional and the constraint mapping to linear spaces ...

This paper is concerned with minimizing a sum of rational functions over a compact set of high dimension. Our approach relies on the second Lasserre hierarchy (also known as the upper bounds hierarchy) formulated on the pushforward measure in order to ...

Conditional gradient methods have attracted much attention in both machine learning and optimization communities recently. These simple methods can guarantee the generation of sparse solutions. In addition, without the computation of full gradients, they ...

We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection, binary quadratic ...

This paper studies bilevel polynomial optimization. We propose a method to solve it globally by using polynomial optimization relaxations. Each relaxation is obtained from the Karush--Kuhn--Tucker (KKT) conditions for the lower level optimization and the ...