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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…
The randomized subspace Newton convex methods for the sensor selection problem are proposed. The randomized subspace Newton algorithm is straightforwardly applied to the convex formulation, and the customized method in which the part of the…
We study online convex optimization in the random order model, recently proposed by \citet{garber2020online}, where the loss functions may be chosen by an adversary, but are then presented to the online algorithm in a uniformly random…
We present a novel methodology for convex optimization algorithm design using ideas from electric RLC circuits. Given an optimization problem, the first stage of the methodology is to design an appropriate electric circuit whose…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine…
In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…
Many practical applications of robotics require systems that can operate safely despite uncertainty. In the context of motion planning, two types of uncertainty are particularly important when planning safe robot trajectories. The first is…
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 this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…
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.…
This article considers nonconvex global optimization problems subject to uncertainties described by continuous random variables. Such problems arise in chemical process design, renewable energy systems, stochastic model predictive control,…
Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…
This paper presents a convex approach to the optimization of a cooperative rendezvous, that is, the problem of two distant spacecraft that simultaneously operate to get closer. Convex programming guarantees convergence towards the optimal…
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…
We study the question of whether parallelization in the exploration of the feasible set can be used to speed up convex optimization, in the local oracle model of computation. We show that the answer is negative for both deterministic and…