Related papers: Global optimality in model predictive control via …
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
We study the problem of designing a controller that satisfies an arbitrary number of affine inequalities at every point in the state space. This is motivated by the fact that a variety of key control objectives, such as stability, safety,…
This paper shows how a class of non-convex optimization problems constrained by discretized nonlinear partial differential equations may be solved to global optimality using an interior point continuation method. The solution procedure…
Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…
In this paper, we propose new proximal Newton-type methods for convex optimization problems in composite form. The applications include model predictive control (MPC) and embedded MPC. Our new methods are computationally attractive since…
We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…
Contemporary global optimization algorithms are based on local measures of utility, rather than a probability measure over location and value of the optimum. They thus attempt to collect low function values, not to learn about the optimum.…
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…
This paper studies the problem of steering a linear time-invariant system subject to state and input constraints towards a goal location that may be inferred only through partial observations. We assume mixed-observable settings, where the…
Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
In the field of global optimization, many existing algorithms face challenges posed by non-convex target functions and high computational complexity or unavailability of gradient information. These limitations, exacerbated by sensitivity to…
Allocation of dynamically-arriving (i.e., online) divisible resources among a set of offline agents is a fundamental problem, with applications to online marketplaces, scheduling, portfolio selection, signal processing, and many other…
Devising efficient algorithms that track the optimizers of continuously varying convex optimization problems is key in many applications. A possible strategy is to sample the time-varying problem at constant rate and solve the resulting…
This paper studies the problem of output agreement in networks of nonlinear dynamical systems under time-varying disturbances. Necessary and sufficient conditions for output agreement are derived for the class of incrementally passive…
Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
Hidden convex optimization is such a class of nonconvex optimization problems that can be globally solved in polynomial time via equivalent convex programming reformulations. In this paper, we focus on checking local optimality in hidden…
In this paper, a convex optimization-based method is proposed for numerically solving dynamic programs in continuous state and action spaces. The key idea is to approximate the output of the Bellman operator at a particular state by the…