arXiv subjects

Nikos Dimou

Publications and source records attributed to Nikos Dimou.

4 recordsLinked to original sources

arXiv2026

A Sequential Cubic Programming Method with Second-Order Complexity Guarantees for Equality Constrained Optimization

We develop a new method for equality constrained optimization problems based on a sequential cubic programming framework. Each iteration utilizes a step decomposition based on the Jacobian of the constraints into a normal and a tangential component, the latter of which is found by solving a subproblem involving cubic regularization. The method incorporates second-order correction steps as necessary to ensure global convergence to second-order stationary points as well as local quadratic convergence. In addition, we show that the algorithm is the first to obtain worst case complexity guarantees on the order of $\mathcal{O}(\epsilon_g^{-3/2})$ for the gradient of the Lagrangian, $\mathcal{O}(\epsilon_H^{-3})$ in terms of second-order stationarity, and $\mathcal{O}(\epsilon_c^{-1})$ in terms of the constraint violation. These are the best known complexity guarantees of any method for this class of problems.

math.OC↗

arXiv2025

Expectation-enforcing strategies for repeated games

Originating in evolutionary game theory, the class of "zero-determinant" strategies enables a player to unilaterally enforce linear payoff relationships in simple repeated games. An upshot of this kind of payoff constraint is that it can shape the incentives for the opponent in a predetermined way. An example is when a player ensures that the agents get equal payoffs. While extensively studied in infinite-horizon games, extensions to discounted games, nonlinear payoff relationships, richer strategic environments, and behaviors with long memory remain incompletely understood. In this paper, we provide necessary and sufficient conditions for a player to enforce arbitrary payoff relationships (linear or nonlinear), in expectation, in discounted games. These conditions characterize precisely which payoff relationships are enforceable using strategies of arbitrary complexity. Our main result establishes that any such enforceable relationship can actually be implemented using a simple two-point reactive learning strategy, which conditions on the opponent's most recent action and the player's own previous mixed action, using information from only one round into the past. For additive payoff constraints, we show that enforcement is possible using even simpler (reactive) strategies that depend solely on the opponent's last move. In other words, this tractable class is universal within expectation-enforcing strategies. As examples, we apply these results to characterize extortionate, generous, equalizer, and fair strategies in the iterated prisoner's dilemma, asymmetric donation game, nonlinear donation game, and the hawk-dove game, identifying precisely when each class of strategy is enforceable and with what minimum discount factor.

econ.TH↗

arXiv2023

Software Development Vehicles to enable extended and early co-design: a RISC-V and HPC case of study

Prototyping HPC systems with low-to-mid technology readiness level (TRL) systems is critical for providing feedback to hardware designers, the system software team (e.g., compiler developers), and early adopters from the scientific community. The typical approach to hardware design and HPC system prototyping often limits feedback or only allows it at a late stage. In this paper, we present a set of tools for co-designing HPC systems, called software development vehicles (SDV). We use an innovative RISC-V design as a demonstrator, which includes a scalar CPU and a vector processing unit capable of operating large vectors up to 16 kbits. We provide an incremental methodology and early tangible evidence of the co-design process that provide feedback to improve both architecture and system software at a very early stage of system development.

cs.OH↗

arXiv2023

On the Equivalence of Zero-Sum Games and Conic Programs

We prove the almost equivalence of the minimax theorem and the strong duality theorem for a large class of games and conic programs. The previous fundamental results on the equivalence of linear programming and two-player zero-sum games with simplex-strategy sets are extended to Banach spaces, and a comprehensive framework unifying two-player zero-sum games and conic linear programs is established. Specifically, we show that for every zero-sum game with a bilinear payoff function and strategy sets that represent bases of convex cones, the minimax equality holds and its game value and Nash equilibria can be found by solving a primal-dual pair of conic programs. Conversely, the minimax theorem for the same class of games "almost always" implies strong duality of conic linear programming. In fact, we give a game-dependent characterization of strict feasibility, and show that minimax is equivalent to a generalized version of Ville's theorem of the alternative. Several well-established game classes are embedded in the introduced model, including (i) semi-infinite, (ii) semidefinite, (iii) quantum, (iv) time-dependent, and (v) polynomial games, as well as (vi) the mixed extension of any continuous game with compact strategy sets.

math.OC↗