SIAM Journal on Optimization

We analyze a convex stochastic optimization problem where the state is assumed to belong to the Bochner space of essentially bounded random variables with images in a reflexive and separable Banach space. For this problem, we obtain optimality conditions ...

Meirowitz [Econom. Lett., 78 (2003), pp. 213--218] showed existence of the continuous Bayesian Nash equilibrium for Bayesian games with continuous type and action spaces under the condition that the best response strategies are equicontinuous. In this ...

We propose an efficient algorithm for finding first-order Nash equilibria in min-max problems of the form $\textstyle\min_{x \in X}\max_{y\in Y} F(x,y)$, where the objective function is smooth in both variables and concave with respect to $y$; the sets $X$...

Here we consider the question whether the lattice reformulation of a linear integer program can be used to produce effective cutting planes. In particular, we aim at deriving split cuts that cut off more of the integrality gap than Gomory mixed-integer (...

This paper presents smoothing schemes for obtaining approximate stationary points of unconstrained or linearly constrained composite nonconvex-concave min-max (and hence nonsmooth) problems by applying well-known algorithms to composite smooth ...

We introduce and prove convergence of a damped Newton algorithm to approximate solutions of the semidiscrete optimal transport problem with storage fees, corresponding to a problem with hard capacity constraints. This is a variant of the optimal transport ...

Low rank matrix recovery problems appear widely in statistics, combinatorics, and imaging. One celebrated method for solving these problems is to formulate and solve a semidefinite program (SDP). It is often known that the exact solution to the SDP with ...

We propose a manifold sampling algorithm for minimizing a nonsmooth composition $f= h\circ F$, where we assume $h$ is nonsmooth and may be inexpensively computed in closed form and $F$ is smooth but its Jacobian may not be available. We additionally assume ...

Second-order sufficient conditions for local optimality have been playing an important role in local convergence analysis of optimization algorithms. In this paper, we demonstrate that this condition alone suffices to justify the linear convergence of the ...

This paper develops a new storage-optimal algorithm that provably solves almost all semidefinite programs (SDPs). This method is particularly effective for weakly constrained SDPs under appropriate regularity conditions. The key idea is to formulate an ...

Block decomposition algorithms decompose the variable vector into multiple blocks and update a single block with other blocks fixed at each iteration. In each epoch, the blocks are updated according to a certain update order. There are at least two ...

Modern large-scale finite-sum optimization relies on two key aspects: distribution and stochastic updates. For smooth and strongly convex problems, existing decentralized algorithms are slower than modern accelerated variance-reduced stochastic algorithms ...

A generalized Nash equilibrium problem corresponds to a noncooperative interaction between a finite set of players in which the cost function and the feasible set of each player depend on the decisions of the others. The classical existence result for ...

In this paper, we complement the framework of bilevel unconstrained minimization (BLUM) [Y. Nesterov, Math. Program., to appear] by a new $p$th-order proximal-point method convergent as $O(k^{-(3p+1)/2})$, where $k$ is the iteration counter. As compared with ...

The objective of the paper is to investigate a dynamical system called a differential variational-hemivariational inequality (DVHVI) which couples an abstract variational-hemivariational inequality of elliptic type and a nonlinear evolution inclusion ...

This paper combines two ingredients in order to get a rather surprising result on one of the most studied, elegant, and powerful tools for solving convex feasibility problems, the method of alternating projections (MAP). Going back to names such as ...

We develop a general methodology for deriving probabilistic guarantees for solutions of robust optimization problems. Our analysis applies broadly to any convex compact uncertainty set and to any constraint affected by uncertainty in a concave manner, under ...

This paper examines a perturbed heavy ball system with vanishing damping that contains a Tikhonov regularization term in connection to the minimization problem of a convex Fréchet differentiable function. We show that the value of the objective function ...

In this paper we provide a generalization of the Douglas--Rachford splitting (DRS) and the primal-dual algorithm [L. Condat, J. Optim. Theory Appl., 158 (2013), pp. 460--479; B. C. Vu͂, Adv. Comput. Math., 38 (2013), pp. 667--681] for solving monotone ...

Inverse optimization is the problem of determining the values of missing input parameters for an associated forward problem that are closest to given estimates and that will make a given target vector optimal. This study is concerned with the relationship ...

Distributionally robust optimization involves various probability measures in its problem formulation. They can be bundled to constitute a risk functional. For this equivalence, risk functionals constitute a fundamental building block in distributionally ...

A novel gradient stepsize is derived at the motivation of equipping the Barzilai--Borwein (BB) method with the two dimensional quadratic termination property. A remarkable feature of the novel stepsize is that its computation only depends on the BB ...

$\ell_{2,1}$ norm minimization with orthogonality constraints, which comprise a feasible region called the Stiefel manifold, has wide applications in statistics and data science. The state-of-the-art approaches adopt a proximal gradient technique on either ...

In derivative-free and blackbox optimization, the objective function is often evaluated through the execution of a computer program seen as a blackbox. It can be stochastic, in the sense that an additive centered Gaussian random noise is present in the ...

We introduce a simplex method for general countably infinite linear programs. Previous literature has focused on special cases, such as infinite network flow problems or Markov decision processes. A novel aspect of our approach is the placing of data and ...

It has been widely recognized that the 0/1-loss function is one of the most natural choices for modelling classification errors, and it has a wide range of applications including support vector machines and 1-bit compressed sensing. Due to the ...

This paper is devoted to the study of the expected-integral multifunctions given in the form ${{E}_{\Phi}}(x):=\int_T\Phi_t(x)d\mu$, where $\Phi\colon T\times\X\;{\lower {$\rightarrow$}}\kern {\raise {$\rightarrow$}}\;\Y$ is a set-valued mapping on a ...