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The optimization problems with simple bounds are an important class of problems. To facilitate the computation of such problems, an unconstrained-like dynamic method, motivated by the Lyapunov control principle, is proposed. This method…
The vast majority of the literature on stochastic semidefinite programs (stochastic SDPs) with recourse is concerned with risk-neutral models. In this paper, we introduce mean-risk models for stochastic SDPs and study structural properties…
Automated synthesis of correct-by-construction controllers for autonomous systems is crucial for their deployment in safety-critical scenarios. Such autonomous systems are naturally modeled as stochastic dynamical models. The general…
In this paper, we propose novel mixed-integer linear programming (MIP) formulations to model decision problems posed as influence diagrams. We also present a novel heuristic that can be employed to warm start the MIP solver, as well as…
Generalized Disjunctive Programming (GDP) provides an alternative framework to model optimization problems with both discrete and continuous variables. The key idea behind GDP involves the use of logical disjunctions to represent discrete…
Program optimization is the process of modifying software to execute more efficiently. Superoptimizers attempt to find the optimal program by employing significantly more expensive search and constraint solving techniques. Generally, these…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
We give the first approximation algorithm for mixed packing and covering semidefinite programs (SDPs) with polylogarithmic dependence on width. Mixed packing and covering SDPs constitute a fundamental algorithmic primitive with recent…
We propose the formulation of convex Generalized Disjunctive Programming (GDP) problems using conic inequalities leading to conic GDP problems. We then show the reformulation of conic GDPs into Mixed-Integer Conic Programming (MICP)…
Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…
Probabilistic control design is founded on the principle that a rational agent attempts to match modelled with an arbitrary desired closed-loop system trajectory density. The framework was originally proposed as a tractable alternative to…
This paper investigates the design of a robust fixed-order controller for single-input-single-output (SISO) polytopic systems with interval uncertainties, with the aim that the closed-loop stability is appropriately ensured and the…
Incremental stability is a property of dynamical systems that ensures the convergence of trajectories with respect to each other rather than a fixed equilibrium point or a fixed trajectory. In this paper, we introduce a related stability…
Nonlinear optimal control problems for trajectory planning with obstacle avoidance present several challenges. While general-purpose optimizers and dynamic programming methods struggle when adopted separately, their combination enabled by a…
Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where…
The problem of deciding whether a set of quantum measurements is jointly measurable is known to be equivalent to determining whether a quantum assemblage is unsteerable. This problem can be formulated as a semidefinite program (SDP).…
This study investigates possibility of placing bounds on the parameters, arising from the non-commutative Snyder space-time model and Generalized Uncertainty Principle (GUP) approach, by utilizing seismic data. We investigate the dependence…
Mixed-integer optimization is at the core of many online decision-making systems that demand frequent updates of decisions in real time. However, due to their combinatorial nature, mixed-integer linear programs (MILPs) can be difficult to…
Modern stochastic optimization pipelines increasingly rely on learned generative models to represent uncertainty, while downstream decisions are evaluated almost entirely through Monte Carlo scenarios. This shifts the operational object of…
With the growth of complexity and extent, large scale interconnected network systems, e.g. transportation networks or infrastructure networks, become more vulnerable towards external disruptions. Hence, managing potential disruptive events…