We propose the moment cone relaxation for a class of polynomial optimization problems (POPs) to extend the results on the completely positive cone programming relaxation for the quadratic optimization (QOP) model by Arima, Kim and Kojima. The moment cone relaxation is constructed to take advantage of sparsity of the POPs, so that efficient numerical methods can be developed in the future. We es...

Reducing the energy consumption of heating, ventilation, and air conditioning (HVAC) systems while ensuring users’ comfort is both academic practical significance. However, the-state-of-the-art optimization model HVAC system that either thermal dynamic simplified as a linear model, or single-timescale, which leads to heavy computation burden. To balance practicality overhead computation, in thi...

In this paper, an adaptive proximal bundle method is proposed for a class of nonconvex and nonsmooth composite problems with inexact information. The are the sum finite convex function information function. For function, we design convexification technique ensure linearization errors its augment to be nonnegative. Then, regarded as approximate primal problem. adopt disaggregate strategy regard ...

Abstract We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. analyze a lifting and decomposition approach into problem without for the in space. Both can be solved very efficiently existing methods outer convexification sum-up-rounding strategies linear programming techniques. The coupling is handled using penalty-...

Abstract The brief history of relaxation in continuum mechanics ranges from early application non-convex plasticity and phase transition formulations to small large strain damage mechanics. However, relaxed are still limited the following sense that their material response lack model softening convexification incremental stress potential is computationally costly. This paper presents a reduced ...

In this article, we derive first-order necessary optimality conditions for a constrained optimal control problem formulated in the Wasserstein space of probability measures. To end, introduce new notion localised metric subdifferential compactly supported measures, and investigate intrinsic linearised Cauchy problems associated to non-local continuity equations. particular, show that when veloc...

Motivated by modern regression applications, in this paper, we study the convexification of a class convex optimization problems with indicator variables and combinatorial constraints on indicators. Unlike most previous work sparse problems, simultaneously consider nonlinear non-separable objective, variables, constraints. Specifically, give hull description epigraph composition one-dimensional...

A Unifying Framework for the Convexification of Mixed-Integer Conic Binary Sets The paper “Conic Mixed-Binary Sets: Convex Hull Characterizations and Applications,” by Fatma Kilinc-Karzan, Simge Kucukyavuz, Dabeen Lee, Soroosh Shafieezadeh-Abadeh, develops a unifying framework convexifying mixed-integer conic binary sets. Many applications in machine-learning operations research give rise to in...