相关论文: Performance Bounds for the Scenario Approach and a…
The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled…
Randomized optimization is an established tool for control design with modulated robustness. While for uncertain convex programs there exist randomized approaches with efficient sampling, this is not the case for non-convex problems.…
This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP algorithm for solving nonlinear optimization…
Sequential Convex Programming (SCP) has recently gained significant popularity as an effective method for solving optimal control problems and has been successfully applied in several different domains. However, the theoretical analysis of…
Chance-constrained programs (CCP) represent a trade-off between conservatism and robustness in optimization. In many CCPs, one optimizes an objective under a probabilistic constraint continuously parameterized by a random vector $\xi$. In…
The scenario approach is a general data-driven algorithm to chance-constrained optimization. It seeks the optimal solution that is feasible to a carefully chosen number of scenarios. A crucial step in the scenario approach is to compute the…
We revisit the so-called sampling and discarding approach used to quantify the probability of constraint violation of a solution to convex scenario programs when some of the original samples are allowed to be discarded. Motivated by two…
We introduce a verification framework to exactly verify the worst-case performance of sequential convex programming (SCP) algorithms for parametric non-convex optimization. The verification problem is formulated as an optimization problem…
Chance-constrained programs (CCPs) provide a powerful modeling framework for decision-making under uncertainty, but their nonconvex feasible regions make them computationally challenging. A widely used convex inner approximation replaces…
Stochastic Constraint Programming (SCP) is an extension of Constraint Programming (CP) used for modelling and solving problems involving constraints and uncertainty. SCP inherits excellent modelling abilities and filtering algorithms from…
Optimization problems involving complex variables, when solved, are typically transformed into real variables, often at the expense of convergence rate and interpretability. This paper introduces a novel formalism for a prominent problem in…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
This paper studies a structured compound stochastic program (SP) involving multiple expectations coupled by nonconvex and nonsmooth functions. We present a successive convex-programming based sampling algorithm and establish its…
In a chance constrained program (CCP), the decision-makers aim to seek the best decision whose probability of violating the uncertainty constraints is within the prespecified risk level. As a CCP is often nonconvex and is difficult to solve…
Chance-constrained programs (CCPs) constitute a difficult class of stochastic programs due to its possible nondifferentiability and nonconvexity even with simple linear random functionals. Existing approaches for solving the CCPs mainly…
This paper proposes distributed algorithms to solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. We adopt a scenario approach by randomly sampling the uncertainty set. To facilitate the…
Chance constrained programming (CCP) refers to a type of optimization problem with uncertain constraints that are satisfied with at least a prescribed probability level. In this work, we study the sample average approximation (SAA) of…
Many optimization problems incorporate uncertainty affecting their parameters and thus their objective functions and constraints. As an example, in chance-constrained optimization the constraints need to be satisfied with a certain…
This paper is concerned with objective value performance of the scenario approach for robust convex optimization. A novel method is proposed to derive probabilistic bounds for the objective value from scenario programs with a finite number…
This work investigates the challenge of ensuring safety guarantees in the presence of uncontrollable agents, whose behaviors are stochastic and depend on both their own and the system's states. We present a neural model predictive control…