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Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
In this paper we consider distributed optimization problems in which the cost function is separable, i.e., a sum of possibly non-smooth functions all sharing a common variable, and can be split into a strongly convex term and a convex one.…
Infinite-dimensional linear conic formulations are described for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, whereas the dual…
We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of…
The paper is devoted to the implicit function theorem involving singular mappings.We also discuss the form of the tangent cone to the solution set of the generalized equations in singular case and give some examples of applications to…
Prediction-correction algorithms are a highly effective class of methods for solving pseudo-convex optimization problems. The descent direction of these algorithms can be viewed as an adjustment to the gradient direction based on the…
One of the most effective algorithms for differentially private learning and optimization is objective perturbation. This technique augments a given optimization problem (e.g. deriving from an ERM problem) with a random linear term, and…
Implicit variables of an optimization problem are used to model variationally challenging feasibility conditions in a tractable way while not entering the objective function. Hence, it is a standard approach to treat implicit variables as…
Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…
A novel class of derivative-free optimization algorithms is developed. The main idea is to utilize certain non-commutative maps in order to approximate the gradient of the objective function. Convergence properties of the novel algorithms…
This paper presents an algorithm to solve non-convex optimal control problems, where non-convexity can arise from nonlinear dynamics, and non-convex state and control constraints. This paper assumes that the state and control constraints…
By introducing a quadratic perturbation to the canonical dual of the maxcut problem, we transform the integer programming problem into a concave maximization problem over a convex positive domain under some circumstances, which can be…
Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…
For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
The usual approach to developing and analyzing first-order methods for smooth convex optimization assumes that the gradient of the objective function is uniformly smooth with some Lipschitz constant $L$. However, in many settings the…
We consider multi-agent, convex optimization programs subject to separable constraints, where the constraint function of each agent involves only its local decision vector, while the decision vectors of all agents are coupled via a common…
We present a model-based derivative-free method for optimization subject to general convex constraints, which we assume are unrelaxable and accessed only through a projection operator that is cheap to evaluate. We prove global convergence…
We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…