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Miguel Martínez-Antón

Publications and source records attributed to Miguel Martínez-Antón.

10 recordsLinked to original sources
arXiv2026

Cooperation in Conic Programming with Applications to Control, Production, and Portfolio

We introduce the class of cooperative conic games, a new family of transferable utility games whose characteristic function can be computed by solving a conic optimization problem. This framework unifies a broad range of optimization-based cooperative games within a common mathematical formulation, encompassing linear, second-order cone, semidefinite, and other convex nonlinear optimization problems admitting conic representations. Exploiting the structural properties of conic programs and conic duality theory, we derive general conditions ensuring the existence of core payoff allocations (or cost shares) and show how such allocations can be computed directly from optimal dual solutions. In particular, the proposed methodology replaces combinatorial verification procedures for core nonemptiness with tractable optimization-based criteria. The expressive power of the framework is illustrated through several representative applications. We show that it models cooperation in multi-agent optimal control, generalizes linear production games to nonlinear production settings such as Cobb--Douglas models, introduces cooperative formulations for portfolio selection under Markowitz, conditional value-at-risk, and entropic risk measures, and unifies a broad class of combinatorial optimization games through exact conic reformulations. These examples involve the most relevant cones in modern convex optimization, highlighting both the versatility of the proposed framework and its potential to strengthen the interaction between mathematical programming and cooperative game theory.

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arXiv2026

Exact Mixed-Integer Conic Liftings for Queueing-Based CDN Design

We study a class of content delivery network design problems in which service performance is explicitly modeled through queueing-based response times. In contrast to standard formulations relying on distance-based approximations, the resulting models incorporate congestion effects and give rise to nonlinear expressions involving ratios of affine mappings, reciprocal terms, and interactions across multiple traffic classes. To address these challenges, we develop a systematic framework based on mixed-integer conic liftings that enables exact reformulations of such expressions within a tractable optimization paradigm. The proposed approach combines McCormick-type envelopes and second-order cone representations to derive mixed-integer conic programming formulations that jointly capture geometric design decisions and stochastic service dynamics within the same system. The framework is first introduced in a single-server setting, where the optimal solution exhibits a connection with the classical Fermat--Weber problem, and is then extended to the multi-server case, leading to a general formulation that simultaneously optimizes server locations, capacity allocation, and routing decisions. Computational experiments on a realistic case study illustrate the impact of congestion-aware modeling on network design and demonstrate the effectiveness of the proposed formulations when solved using modern conic optimization solvers.

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arXiv2026

Exponential Conic Optimization for Multi-Regime Service System Design under Congestion and Tail-Risk Control

We study the design of single-facility service systems operating under multiple recurring regimes with service-level constraints on response times. Regime-dependent arrival and service rates induce hyperexponential response-time distributions, and the design problem selects regime-specific capacities to balance cost, congestion, fairness, and reliability. We propose a mixed-integer exponential conic optimization framework integrating SLA chance constraints, conflict-graph design restrictions, and CVaR-based tail-risk control. Although NP-hard, the problem admits an efficient decomposition scheme and tractable special cases. Computational experiments and a large-scale urban case study show substantial improvements over the current system, quantifying explicit trade-offs between efficiency, congestion control, fairness, and robustness. The framework provides a practical tool for congestion-aware and tail-control service system design.

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arXiv2025

Structural and Solution Analysis for the Ordered Weber Problem under Spatial Uncertainty

We propose a general analytical framework for single-facility continuous location problems under spatial demand uncertainty. In contrast to classical formulations based on discrete or regionally aggregated demands, the proposed model represents uncertainty through general probability measures on $\R^d$, thereby encompassing finite, bounded, and unbounded support distributions within a unified formulation. The objective aggregates expected distances by means of an ordered weighted averaging operator, providing a flexible mathematical structure that includes the classical Weber problem and its ordered extensions as special cases. We establish fundamental properties of this stochastic ordered Weber model, including convexity, continuity, and existence of optimal solutions, and we derive quantitative bounds on the proximity between stochastic minimizers and the convex hulls of demand supports. Building upon these results, we develop and analyze an adaptive sample average approximation scheme, proving its convergence and deriving finite-sample error estimates under mild regularity conditions. For spherically symmetric distributions, we further obtain explicit analytical expressions for the approximation error. Together, these results provide a rigorous mathematical foundation for a broad class of stochastic ordered location models and highlight new theoretical connections between convex analysis, stochastic programming, and ordered optimization.

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arXiv2025

On the Strength of Linear Relaxations in Ordered Optimization

We study the conditions under which the convex relaxation of a mixed-integer linear programming formulation for ordered optimization problems, where sorting is part of the decision process, yields integral optimal solutions. Thereby solving the problem exactly in polynomial time. Our analysis identifies structural properties of the input data that influence the integrality of the relaxation. We show that incorporating ordered components introduces additional layers of combinatorial complexity that invalidate the exactness observed in classical (non-ordered) settings. In particular, for certain ordered problems such as the min--max case, the linear relaxation never recovers the integral solution. These results clarify the intrinsic hardness introduced by sorting and reveal that the strength of the relaxation depends critically on the ``proximity'' of the ordered problem to its classical counterpart: problems closer to the non-ordered case tend to admit tighter relaxations, while those further away exhibit substantially weaker behavior. Computational experiments on benchmark instances confirm the predictive value of the integrality conditions and demonstrate the practical implications of exact relaxations for ordered location problems.

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arXiv2025

On the Complexity of p-Order Cone Programs

This manuscript explores novel complexity results for the feasibility problem over $p$-order cones, extending the foundational work of Porkolab and Khachiyan. By leveraging the intrinsic structure of $p$-order cones, we derive refined complexity bounds that surpass those obtained via standard semidefinite programming reformulations. Our analysis not only improves theoretical bounds but also provides practical insights into the computational efficiency of solving such problems. In addition to establishing complexity results, we derive explicit bounds for solutions when the feasibility problem admits one. For infeasible instances, we analyze their discrepancy quantifying the degree of infeasibility. Finally, we examine specific cases of interest, highlighting scenarios where the geometry of $p$-order cones or problem structure yields further computational simplifications. These findings contribute to both the theoretical understanding and practical tractability of optimization problems involving $p$-order cones.

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arXiv2025

Optimal Mediated Graphs: The role of Combinatorics in Conic Optimization

In this paper, we provide a unified definition of mediated graph, a combinatorial structure with multiple applications in mathematical optimization. We study some geometric and algebraic properties of this family of graphs and analyze extremal mediated graphs under the partial order induced by the cardinalty of their vertex sets. We derive mixed integer linear formulations to compute these challenging graphs and show that these structures are crucial in different fields, such as sum of squares decomposition of polynomials and second-order cone representations of convex cones, with a direct impact on conic optimization. We report the results of an extensive battery of experiments to show the validity of our approaches.

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arXiv2023

On minimal extended representations of generalized power cones

In this paper, we analyze minimal representations of $(p,\boldsymbolα)$-power cones as simpler cones. We derive some new results on the complexity of the representations, and we provide a procedure to construct a minimal representation by means of second order cones in case $\boldsymbolα$ and $p$ are rational. The construction is based on the identification of the cones with a graph, the mediated graph. Then, we develop a mixed integer linear optimization formulation to obtain the optimal mediated graph, and then, the minimal representation. We present the results of a series of computational experiments in order to analyze the computational performance of the approach, both to obtain the representation and its incorporation into a practical conic optimization model that arises in facility location.

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arXiv2023

Optimal coverage-based placement of static leak detection devices for pipeline water supply networks

In this paper, we provide a mathematical optimization-based framework to determine the location of leak detection devices along a network. Assuming that the devices are endowed with a known coverage area, we analyze two different models. The first model aims to minimize the number of devices to be located in order to (fully or partially) cover the volume of the network. In the second model, the number of devices is given, and the goal is to locate them to provide a coverage volume as broad as possible. Unlike other approaches in the literature, in our models, it is not assumed that the devices are located on the network (nodes or edges) but in the whole space and that the different segments in the networks may be partially covered, which allows for more flexible coverage. We also derive a method to construct initial solutions as well as a math-heuristic approach for solving the problem for larger instances. We report the results of a series of experiments on real-world water supply pipeline networks, supporting the validity of our models.

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