August 2026 – Page 2 – Optimization Online

Coordinate Optimality Reformulation for Mixed-Integer Convex Programs with Indicators

Published: 2026/08/02

(Mixed) Integer Nonlinear Programming, Quadratic Programming disjunctive optimization, indicator constraints, mixed-integer convex programming

We consider mixed-integer convex optimization problems in which binary indicators control continuous variables. We introduce the Coordinate Optimality Reformulation (CORe) framework, which augments standard indicator formulations by incorporating coordinate-wise optimality information. The resulting reformulations preserve global optimality while substantially improving branch-and-bound performance, particularly in sparse and structured settings where the coordinate-wise optimality conditions expose exploitable … Read more

A true single–level reformulation for pessimistic bilevel optimization

Published: 2026/08/01

Bilevel Optimization optimality conditions, pessimistic bilevel optimization, single-level reformulation

We propose a single-level reformulation (SLR) for pessimistic bilevel optimization that does not rely on complementarity conditions or optimal value functions. For this reason, we refer to it as a true single-level reformulation (tSLR). A remarkable consequence is that this formulation can satisfy the classical linear independence constraint qualification, despite the fact that even the … Read more

Optimal Route Planning for Orienteering: Branch-and-Cut with Terrain Cost Surfaces and Fatigue

Published: 2026/08/01

Pablo Borrego Ramos

(Mixed) Integer Linear Programming, Branch and Cut Algorithms, Transportation

We address the problem of optimal route planning for competitive orien- teering on real terrain. A Geographic Information System (GIS) pipeline transforms orienteering map data and digital terrain models into a fully asymmetric cost matrix that captures directional slope costs (via the Minetti metabolic model) and cumulative athlete fatigue. The resulting problem, the Asymmetric Orienteering … Read more

A Complete Characterization of Optimal Subgradient Methods for Lipschitz Convex Minimization

Published: 2026/08/01

Nonsmooth Optimization, Semi-definite Programming algorithm design, performance estimation

We consider the design of optimal fixed-step first-order methods for $M$-Lipschitz convex optimization given $\|x_0-x_\star\|\leq D$. Prior works have identified several distinct fixed-step methods, parameterized by a matrix of stepsizes $W$, with the (information-theoretic) minimax optimal rate $MD/\sqrt{N+1}$ of objective gap convergence. We provide a complete characterization of every optimal fixed-step method. Moreover, we show … Read more